. Proof, It is obvious that any node v ? V that does not satisfy properties (a)a n d (b) is enabled and when v executes rule [R] during r 0 , v will satisfy both of these properties because v.m new = null or v.m new ? N (v)andv.s new = ? or |v

. Proof, A node executing rule [R3] four times would execute rule [R6] at least three times, R4] at most 6?d(v) times, i.e. it changes from state In to state Wait at most 6?d(v) times

[. Afek and G. M. Brown, Self-stabilization over unreliable communication media, Distributed Computing, pp.27-34, 1993.
DOI : 10.1007/BF02278853

M. [. Arora and . Gouda, Closure and convergence: a foundation of fault-tolerant computing. Software Engineering, IEEE Transactions on, vol.19, issue.11, pp.1015-1027, 1993.

[. Awerbuch, B. Patt-shamir, G. Varghese, and S. Dolev, Self-stabilization by local checking and global reset (extended abstract), WDAG, pp.326-339, 1994.

K. Andreev and H. Räcke, Balanced graph partitioning, Proceedings of the sixteenth annual ACM symposium on Paral lelism in algorithms and architectures, SPAA '04, pp.120-124, 2004.

[. Awerbuch and M. Sipser, Dynamic networks are as fast as static networks, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.206-219, 1988.
DOI : 10.1109/SFCS.1988.21938

M. Khaled, . Alzoubi, O. Peng-jun-wan, and . Frieder, Maximal independent set, weakly-connected dominating set, and induced spanners in wireless ad hoc networks, International Journal of Foundations of Computer Science, vol.14, issue.109, pp.287-303, 2003.

[. Belkouch, M. Bui, L. Chen, and A. Datta, Self-Stabilizing Deterministic Network Decomposition, Journal of Parallel and Distributed Computing, vol.62, issue.4, pp.696-714, 2002.
DOI : 10.1006/jpdc.2001.1811

[. Bein, A. Kumar-datta, C. R. Jagganagari, and V. Villain, A Self-stabilizing Link-Cluster Algorithm in Mobile Ad Hoc Networks, 8th International Symposium on Parallel Architectures,Algorithms and Networks (ISPAN'05), pp.436-441, 2005.
DOI : 10.1109/ISPAN.2005.12

J. Blum, M. Ding, A. Thaeler, and X. Cheng, Connected Dominating Set in Sensor Networks and MANETs, Handbook of Combinatorial Optimization, pp.329-369, 2005.
DOI : 10.1007/0-387-23830-1_8

S. [. Bryant, C. El-zanati, and . Eynden, Star factorizations of graph products, Journal of Graph Theory, vol.17, issue.168, pp.59-66, 2001.
DOI : 10.1002/1097-0118(200102)36:2<59::AID-JGT1>3.0.CO;2-A

S. [. Berns and . Ghosh, Dissecting self-* properties In Self-Adaptive and Self-Organizing Systems, SASO '09. Third IEEE International Conference on, pp.10-19, 2009.

R. S. Jean, F. Blair, and . Manne, An efficient self-stabilizing distance-2 coloring algorithm, Theoretical Computer Science, vol.444, issue.0, pp.28-39

N. [. Bendjoudi, E. Melab, and . Talbi, P2P design and implementation of a parallel branch and bound algorithm for grids, International Journal of Grid and Utility Computing, vol.1, issue.2, pp.159-168, 2009.
DOI : 10.1504/IJGUC.2009.022031
URL : https://hal.archives-ouvertes.fr/hal-00690313

T. Bar-noy, . Brown, P. Matthew, T. L. Johnson, O. Porta et al., Assigning Sensors to Missions with Demands, Algorithmic Aspects of Wireless Sensor Networks, pp.114-125
DOI : 10.1007/978-3-540-77871-4_11

[. Boulinier, F. Petit, and V. Villain, When graph theory helps self-stabilization, Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing , PODC '04, pp.150-159, 2004.
DOI : 10.1145/1011767.1011790

[. Belhoul, S. Yahiaoui, and H. Kheddouci, Efficient self-stabilizing algorithms for minimal total k-dominating sets in graphs, Information Processing Letters, vol.114, issue.7, pp.339-343, 2014.
DOI : 10.1016/j.ipl.2014.02.002
URL : https://hal.archives-ouvertes.fr/hal-01270709

]. P. Cai74 and . Cain, Decomposition of complete graphs into stars, Bull. Austral. Math. Soc, vol.10, issue.68, pp.23-30, 1974.

Y. Well, C. Chiu, S. Chen, and . Tsai, A 4n-move selfstabilizing algorithm for the minimal dominating set problem using an unfair distributed daemon, Information Processing Letters, vol.114, issue.25, pp.515-518, 2014.

[. Caron, A. Kumar-datta, B. Depardon, and L. L. Larmore, A Self-stabilizing K-Clustering Algorithm Using an Arbitrary Metric, Euro-Par, pp.602-614, 2009.
DOI : 10.1109/71.588622
URL : https://hal.archives-ouvertes.fr/inria-00440276

[. Chattopadhyay, L. Higham, and K. Seyffarth, Dynamic and self-stabilizing distributed matching, Proceedings of the twenty-first annual symposium on Principles of distributed computing , PODC '02, pp.290-297, 2002.
DOI : 10.1145/571825.571877

A. Caprara and R. Rizzi, Packing triangles in bounded degree graphs, Information Processing Letters, vol.84, issue.4, pp.175-180, 2002.
DOI : 10.1016/S0020-0190(02)00274-0

R. Vadim-drabkin, M. Friedman, and . Gradinariu, Self-stabilizing Wireless Connected Overlays, Proceedings of the 10th International Conference on Principles of Distributed Systems, OPODIS'06, pp.425-439, 2006.
DOI : 10.1007/11945529_30

S. Gayla, . Domke, H. Johannes, . Hattingh, R. Lisa et al., On parameters related to strong and weak domination in graphs, Discrete Mathematics, vol.258, issue.1, pp.1-11, 2002.

]. S. Dhr-+-11, K. Devismes, Y. Heurtefeux, A. K. Rivierre, L. L. Datta et al., Self-stabilizing small k-dominating sets, Networking and Computing (ICNC), 2011 Second International Conference on, pp.30-39

W. Edsger and . Dijkstra, Self-stabilizing systems in spite of distributed control, Commun. ACM, vol.17, issue.11, pp.643-644, 1974.

S. Dolev, A. Israeli, and S. Moran, Self-stabilization of dynamic systems assuming only read/write atomicity, Distributed Computing, pp.3-16, 1993.
DOI : 10.1007/BF02278851

[. Dong, Y. Liu, and X. Liao, Self-monitoring for sensor networks, Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing , MobiHoc '08, pp.431-440, 2008.
DOI : 10.1145/1374618.1374675

X. Dong, Y. Liao, C. Liu, X. Shen, and . Wang, Edge self-monitoring for wireless sensor networks. Parallel and Distributed Systems, IEEE Transactions on, vol.22, issue.100, pp.514-527, 2011.

K. Ajoy, L. L. Datta, P. Larmore, and . Vemula, A selfstabilizing o(k)-time k-clustering algorithm, Comput. J, vol.53, issue.3, pp.342-350, 2010.

R. [. Delouille, R. G. Neelamani, and . Baraniuk, Robust Distributed Estimation Using the Embedded Subgraphs Algorithm, IEEE Transactions on Signal Processing, vol.54, issue.8, pp.2998-3010, 2006.
DOI : 10.1109/TSP.2006.874839

R. [. Delouille, V. Neelamani, R. G. Chandrasekaran, and . Baraniuk, The embedded triangles algorithm for distributed estimation in sensor Bibliography networks, Statistical Signal Processing, pp.371-374, 2003.

S. Dolev, Self Stabilization, Journal of Aerospace Computing, Information, and Communication, vol.1, issue.6, 2000.
DOI : 10.2514/1.10141
URL : https://hal.archives-ouvertes.fr/inria-00627780

[. Dubois and S. Tixeuil, A taxonomy of daemons in selfstabilization, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00628390

[. Ding, Z. James, . Wang, K. Pradip, and . Srimani, A Linear Time Self-stabilizing Algorithm for Minimal Weakly Connected Dominating Sets, International Journal of Parallel Programming, vol.72, issue.1, pp.1-12, 2014.
DOI : 10.1007/s10766-014-0335-4

[. Ding, J. Wang, K. Pradip, and . Srimani, Self-Stabilizing Algorithms for Maximal 2-packing and General k-packing (k ??? 2) with Safe Convergence in an Arbitrary Graph, International Journal of Networking and Computing, vol.5, issue.1, pp.105-121
DOI : 10.15803/ijnc.5.1_105

[. Ding, F. Xie, and Q. Wu, Energy-balanced clustering with Master/Slave method for wireless sensor networks, 2009 9th International Conference on Electronic Measurement & Instruments, pp.3-20, 2009.
DOI : 10.1109/ICEMI.2009.5274324

G. [. Foggia, C. Percannella, M. Sansone, and . Vento, Benchmarking graph-based clustering algorithms, Image and Vision Computing, vol.27, issue.7, pp.979-988, 2009.
DOI : 10.1016/j.imavis.2008.05.002

C. Felix and . Gärtner, A survey of self-stabilizing spanning-tree construction algorithms, 2003.

[. Ganeriwal, L. K. Balzano, and M. B. Srivastava, Reputation-based framework for high integrity sensor networks, ACM Trans. Sen. Netw, vol.415, issue.3, pp.1-15, 2008.

G. Gairing, W. Goddard, S. T. Hedetniemi, P. Kristiansen, and A. A. Mcrae, DISTANCE-TWO INFORMATION IN SELF-STABILIZING ALGORITHMS, Parallel Processing Letters, vol.14, issue.03n04, pp.387-398, 2004.
DOI : 10.1142/S0129626404001970

G. Goddard, S. T. Hedetniemi, D. P. Jacobs, P. K. Srimani, and Z. Xu, Self-stabilizing graph protocols. Parallel Processing Letters, pp.189-199, 2008.

[. Goddard, S. T. Hedetniemi, D. P. Jacobs, K. Pradip, and . Srimani, A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system graph, Proceedings International Parallel and Distributed Processing Symposium, pp.240-243, 2003.
DOI : 10.1109/IPDPS.2003.1213437

[. Goddard, S. T. Hedetniemi, D. P. Jacobs, and P. K. Srimani, A robust distributed generalized matching protocol that stabilizes in linear time, 23rd International Conference on Distributed Computing Systems Workshops, 2003. Proceedings., pp.461-465, 2003.
DOI : 10.1109/ICDCSW.2003.1203595

[. Goddard, S. T. Hedetniemi, D. P. Jacobs, and P. K. Srimani, Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks, Proceedings International Parallel and Distributed Processing Symposium, pp.22-28, 2003.
DOI : 10.1109/IPDPS.2003.1213302

W. Goddard, S. T. Hedetniemi, D. P. Jacobs, and P. K. Srimani, Self-Stabilizing Global Optimization Algorithms for Large Network Graphs, International Journal of Distributed Sensor Networks, vol.63, issue.1, pp.329-344, 2005.
DOI : 10.1080/15501320500330745

W. Goddard, S. T. Hedetniemi, D. P. Jacobs, and V. Trevisan, Distance- k knowledge in self-stabilizing algorithms, Theoretical Computer Science, vol.399, issue.1-2, pp.118-127, 2008.
DOI : 10.1016/j.tcs.2008.02.009

W. Goddard, S. T. Hedetniemi, and Z. Shi, An anonymous selfstabilizing algorithm for 1-maximal matching in trees, Information Processing Letters, vol.91, issue.24, pp.797-803, 2006.

A. Gibbons, Algorithmic Graph Theory, 1985.

R. Michael, D. S. Garey, and . Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979.

H. Guellati and . Kheddouci, A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs, Journal of Parallel and Distributed Computing, vol.70, issue.4, pp.406-415, 2010.
DOI : 10.1016/j.jpdc.2009.11.006

P. [. Goddard and . Srimani, Anonymous self-stabilizing distributed algorithms for connected dominating set in a network graph, Proceedings of the international multi-conference on complexity, p.2010

M. Gradinariu and S. Tixeuil, Conflict managers for selfstabilization without fairness assumption, Proceedings of the 27th International Conference on Distributed Computing Systems, ICDCS '07, p.46, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01336216

B. Hauck, Time-and Space-Efficient Self-Stabilizing Algorithms. Dissertation, pp.20-100

C. Tetz, C. Huang, C. Chen, and . Wang, A linear-time self-stabilizing algorithm for the minimal 2-dominating set problem in general networks, J. Inf. Sci. Eng, vol.24, issue.28, pp.175-187, 2008.

]. T. Her02 and . Herman, A comprehensive bibliography on self-stabilization, Theoretical Computer Science, Chicago J, 2002.

[. Hsu and S. Huang, A self-stabilizing algorithm for maximal matching, Information Processing Letters, vol.43, issue.2, pp.77-81, 1992.
DOI : 10.1016/0020-0190(92)90015-N

S. [. Hedetniemi, D. P. Hedetniemi, P. K. Jacobs, and . Srimani, Self-stabilizing algorithms for minimal dominating sets and maximal independent sets, Computers & Mathematics with Applications, vol.46, issue.5-6, pp.805-811, 2003.
DOI : 10.1016/S0898-1221(03)90143-X

T. Stephen, D. P. Hedetniemi, P. K. Jacobs, and . Srimani, Maximal matching stabilizes in time o(m), Inf. Process. Lett, vol.80, issue.5, pp.221-223, 2001.

C. Tetz, J. Huang, C. Lin, C. Chen, and . Wang, A self-stabilizing algorithm for finding a minimal 2-dominating set assuming the distributed demon model, Computers and Mathematics with Applications, vol.54, issue.28, pp.350-356, 2007.

H. Ishii and H. Kakugawa, A self-stabilizing algorithm for finding cliques in distributed systems, 21st IEEE Symposium on Reliable Distributed Systems, 2002. Proceedings., p.390, 2002.
DOI : 10.1109/RELDIS.2002.1180216

S. [. Ikeda, H. Kamei, and . Kakugawa, A space-optimal self-stabilizing algorithm for the maximal independent set problem, Proc. 3rd International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT), pp.70-74, 2002.

K. Ioannidou, Transformations of Self-Stabilizing Algorithms, Distributed Computing, pp.103-117, 2002.
DOI : 10.1007/3-540-36108-1_7

A. Jain and A. Gupta, A distributed self-stabilizing algorithm for finding a connected dominating set in a graph, Parallel and Distributed Computing, Applications and Technologies, 2005. PDCAT 2005. Sixth International Conference on, pp.615-619, 2005.

F. [. Johnen and . Mekhaldi, Self-Stabilizing Computation and Preservation of Knowledge of Neighbor Clusters, 2011 IEEE Fifth International Conference on Self-Adaptive and Self-Organizing Systems, pp.41-50, 2011.
DOI : 10.1109/SASO.2011.15
URL : https://hal.archives-ouvertes.fr/hal-00647854

C. Johnen and F. Mekhaldi, Self-stabilizing with service guarantee construction of 1-hop weight-based bounded size clusters, Journal of Parallel and Distributed Computing, vol.74, issue.1, pp.1900-1913, 2014.
DOI : 10.1016/j.jpdc.2013.09.004
URL : https://hal.archives-ouvertes.fr/hal-00939445

C. Johnen, Memory efficient, self-stabilizing algorithm to construct BFS spanning trees, Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing , PODC '97, 1997.
DOI : 10.1145/259380.259508
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.1830

S. [. Khalil, C. Bagchi, and . Nina-rotaru, DICAS: Detection, Diagnosis and Isolation of Control Attacks in Sensor Networks, First International Conference on Security and Privacy for Emerging Areas in Communications Networks (SECURECOMM'05), pp.89-100, 2005.
DOI : 10.1109/SECURECOMM.2005.17

[. Khalil, S. Bagchi, and N. B. Shroff, Liteworp: A lightweight countermeasure for the wormhole attack, Multihop Wireless Network. In the International Conference on Dependable Systems and Networks (DSN, pp.612-621, 2005.

]. J. Kes88 and . Kessels, An exercise in proving self-stabilization with a variant function, Inf. Process. Lett, vol.29, issue.20, pp.39-42, 1988.

]. D. Kh78a, P. Kirkpatrick, and . Hell, On the completeness of a generalized matching problem, STOC, pp.240-245, 1978.

G. David, P. Kirkpatrick, and . Hell, On the completeness of a generalized matching problem, Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, STOC '78, pp.240-245, 1978.

P. [. Kirkpatrick and . Hell, On the Complexity of General Graph Factor Problems, SIAM Journal on Computing, vol.12, issue.3, pp.601-609, 1983.
DOI : 10.1137/0212040

H. [. Kamei and . Kakugawa, A self-stabilizing algorithm for the distributed minimal k-redundant dominating set problem in tree networks, Proceedings of the 8th International Scientific and Practical Conference of Students, Post-graduates and Young Scientists. Modern Technique and Technologies. MTT'2002 (Cat. No.02EX550), pp.720-724, 2003.
DOI : 10.1109/PDCAT.2003.1236399

[. Kamei and H. Kakugawa, A Self-Stabilizing Approximation Algorithm for the Distributed Minimum k-Domination, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.88, issue.5, pp.88-1109, 2005.
DOI : 10.1093/ietfec/e88-a.5.1109

H. [. Kamei and . Kakugawa, A self-stabilizing approximation algorithm for the minimum weakly connected dominating set with safe convergence, Proceedings of the 1st International Workshop on Reliability , Availability, and Security (WRAS), pp.5766-5793, 2007.

[. Kamei and H. Kakugawa, A Self-stabilizing Approximation for the Minimum Connected Dominating Set with Safe Convergence
DOI : 10.1016/S0898-1221(03)90143-X

[. Kamei and H. Kakugawa, A SELF-STABILIZING DISTRIBUTED APPROXIMATION ALGORITHM FOR THE MINIMUM CONNECTED DOMINATING SET, International Journal of Foundations of Computer Science, vol.21, issue.03, pp.459-476, 2010.
DOI : 10.1142/S0129054110007362

[. Kakugawa and T. Masuzawa, Convergence Time Analysis of Self-stabilizing Algorithms in Wireless Sensor Networks with Unreliable Links, Stabilization , Safety, and Security of Distributed Systems, pp.173-187, 2008.
DOI : 10.1016/0020-0190(91)90111-T

F. Kuhn, T. Moscibroda, and R. Wattenhofer, Initializing newly deployed ad hoc and sensor networks, Proceedings of the 10th annual international conference on Mobile computing and networking , MobiCom '04, pp.260-274, 2004.
DOI : 10.1145/1023720.1023746

S. Katz and K. J. Perry, Self-stabilizing extensions for message-passing systems, Proceedings of the ninth annual ACM symposium on Principles of distributed computing , PODC '90, pp.17-26, 1993.
DOI : 10.1145/93385.93405

K. [. Karaata and . Saleh, A distributed self-stabilizing algorithm for finding maximum matching, Computer Systems Science and Engineering, vol.3, pp.175-180, 2000.

A. D. Kshemkalyani and M. Singhal, Distributed Computing: Principles, Algorithms, and Systems, 2008.
DOI : 10.1017/CBO9780511805318

]. L. Lam84 and . Lamport, Solved problems unsolved problems and non-problems in concurrency, PODC, pp.1-11, 1984.

[. Lee and Y. Choi, A resilient packet-forwarding scheme against maliciously packet-dropping nodes in sensor networks, Proceedings of the fourth ACM workshop on Security of ad hoc and sensor networks , SASN '06, pp.59-70, 2006.
DOI : 10.1145/1180345.1180353

[. Lemmouchi, M. Haddad, and H. Kheddouci, Study of robustness of community emerged from exchanges in networks communication, Proceedings of the International Conference on Management of Emergent Digital EcoSystems, MEDES '11, pp.189-196, 2011.
DOI : 10.1145/2077489.2077525

[. Lemmouchi, M. Haddad, and H. Kheddouci, Robustness study of emerged communities from exchanges in peer-to-peer networks, Computer Communications, vol.36, issue.10-11, pp.1145-1158, 2013.
DOI : 10.1016/j.comcom.2013.03.006
URL : https://hal.archives-ouvertes.fr/hal-01339170

. [. Lee, . Ch, and . Lin, Balanced star decompositions of regular multigraphs and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>??</mml:mi></mml:math>-fold complete bipartite graphs, Discrete Mathematics, vol.301, issue.2-3, pp.195-206, 2005.
DOI : 10.1016/j.disc.2005.04.023

. Ch, T. Lin, and . Shyu, A necessary and sufficient condition for the star decomposition of complete graphs, J. Graph Theory, vol.23, issue.4, pp.361-364, 1996.

[. Kuszner, Source code homepage, 2005.

[. Merly and N. Gnanadhas, Linear star decomposition of lobster, Int. J. of Contemp. Math. Sciences, vol.7, issue.6, pp.251-261

[. Marti, J. Thomas, K. Giuli, M. Lai, and . Baker, Mitigating routing misbehavior in mobile ad hoc networks, Proceedings of the 6th annual international conference on Mobile computing and networking , MobiCom '00, pp.255-265, 2000.
DOI : 10.1145/345910.345955

[. Manne and M. Mjelde, A Self-stabilizing Weighted Matching Algorithm, SSS, pp.383-393, 2007.
DOI : 10.1007/978-3-540-76627-8_29

[. Manne, M. Mjelde, L. Pilard, and S. Tixeuil, A new self-stabilizing maximal matching algorithm, SIROCCO, pp.96-108, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00127899

[. Manne, M. Mjelde, L. Pilard, and S. Tixeuil, A new self-stabilizing maximal matching algorithm, Theoretical Computer Science, vol.410, issue.14, pp.1336-1345, 2009.
DOI : 10.1016/j.tcs.2008.12.022
URL : https://hal.archives-ouvertes.fr/inria-00127899

M. Mezmaz, N. Melab, and E. Talbi, A Grid-based Parallel Approach of the Multi-Objective Branch and Bound, 15th EUROMICRO International Conference on Parallel, Distributed and Network-Based Processing (PDP'07), pp.23-30, 2007.
DOI : 10.1109/PDP.2007.7
URL : https://hal.archives-ouvertes.fr/hal-00684833

[. Neggazi, M. Haddad, and H. Kheddouci, Self-stabilizing Algorithm for Maximal Graph Partitioning into Triangles, Proceedings of the 14th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS, pp.31-42
DOI : 10.1007/978-3-642-33536-5_3
URL : https://hal.archives-ouvertes.fr/hal-01353073

[. Neggazi, M. Haddad, V. Turau, and H. Kheddouci, A Self-stabilizing Algorithm for Edge Monitoring Problem, Stabilization, Safety, and Security of Distributed Systems, pp.93-105
DOI : 10.1007/978-3-319-11764-5_7
URL : https://hal.archives-ouvertes.fr/hal-01301092

[. Neggazi, V. Turau, M. Haddad, and H. Kheddouci, A self-stabilizing algorithm for maximal p-star decomposition of general graphs, SSS, pp.74-85
URL : https://hal.archives-ouvertes.fr/hal-01339275

S. Ozkan and C. A. Rodger, Hamilton decompositions of graphs with primitive complements, Discrete Mathematics, vol.309, issue.14, pp.4883-4888, 2009.
DOI : 10.1016/j.disc.2008.07.026

]. C. Pap94 and . Papadimitriou, Computational Complexity, 1994.

A. Pothen, Graph Partitioning Algorithms with Applications to Scientific Computing, 1997.
DOI : 10.1007/978-94-011-5412-3_12

H. Rowaihy, S. Eswaran, M. Johnson, D. Verma, A. Bar-noy et al., A survey of sensor selection schemes in wireless sensor networks, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, p.22, 2007.

H. Raei, M. Tabibzadeh, B. Ahmadipoor, and S. Saei, A self-stabilizing distributed algorithm for minimum connected dominating sets in wireless sensor networks with different transmission ranges, Advanced Communication Technology, 11th International Conference on, pp.526-530, 2009.

[. Serrour, A. Arenas, and S. Gomez, Detecting communities of triangles in complex networks using spectral optimization, Computer Communications, vol.34, issue.5, pp.629-634, 2011.
DOI : 10.1016/j.comcom.2010.05.006

W. [. Shi, S. T. Goddard, and . Hedetniemi, An anonymous self-stabilizing algorithm for 1-maximal independent set in trees, Information Processing Letters, vol.91, issue.2, pp.77-83, 2004.
DOI : 10.1016/j.ipl.2004.03.010

[. Shyu, Decomposition of complete graphs into paths and stars, Discrete Mathematics, vol.310, issue.15-16, pp.3102164-2169, 1516.
DOI : 10.1016/j.disc.2010.04.009

[. Sampathkumar and L. Latha, Strong weak domination and domination balance in a graph, Discrete Mathematics, vol.161, issue.1-3, pp.235-242, 1996.
DOI : 10.1016/0012-365X(95)00231-K

K. Sandeep, . Shukla, J. Daniel, . Rosenkrantz, and . Ravi, Observations on self-stabilizing graph algorithms for anonymous networks, Proceedings of the second workshop on self-stabilizing systems, pp.15-28, 1995.

A. Saito and M. Watanbe, Graph partitioning into induced stars, Ars Combinatoria, vol.36, pp.3-6, 1993.

Z. [. Srimani and . Xu, Self-Stabilizing Algorithms of Constructing Spanning Tree and Weakly Connected Minimal Dominating Set, 27th International Conference on Distributed Computing Systems Workshops (ICDCSW'07), pp.3-3, 2007.
DOI : 10.1109/ICDCSW.2007.73

G. Tel, Introduction to Distributed Algorithms, 1994.
DOI : 10.1017/CBO9781139168724

G. Tel, Maximal matching stabilizes in quadratic time, Information Processing Letters, vol.49, issue.6, pp.271-272, 1994.
DOI : 10.1016/0020-0190(94)90098-1

V. Turau and B. Hauck, A self-stabilizing algorithm for constructing weakly connected minimal dominating sets, Information Processing Letters, vol.109, issue.14, pp.763-767, 2009.
DOI : 10.1016/j.ipl.2009.03.013

V. Turau and B. Hauck, A new analysis of a self-stabilizing maximum weight matching algorithm with approximation ratio 2, Theoretical Computer Science, vol.412, issue.40, pp.5527-5540, 2011.
DOI : 10.1016/j.tcs.2010.11.032

O. Theel, Exploitation of ljapunov theory for verifying selfstabilizing algorithms, Distributed Computing (DISC), pp.209-222, 1914.

[. Tixeuil, Algorithms and Theory of Computation Handbook, Second Edition, chapter Self-stabilizing Algorithms, 2009.

V. Turau, Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler, Information Processing Letters, vol.103, issue.3, pp.88-93, 2007.
DOI : 10.1016/j.ipl.2007.02.013

V. Turau, Efficient transformation of distance-2 self-stabilizing algorithms, Journal of Parallel and Distributed Computing, vol.72, issue.4, pp.603-612
DOI : 10.1016/j.jpdc.2011.12.008

V. [. Unterschutz and . Turau, Construction of connected dominating sets in large-scale MANETs exploiting self-stabilization, 2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS), pp.1-6, 2011.
DOI : 10.1109/DCOSS.2011.5982201

[. Wu and R. Srikant, Regulated maximal matching: A distributed scheduling algorithm for multi-hop wireless networks with node-exclusive spectrum sharing, Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on, pp.5342-5347, 2005.

[. Xu, S. T. Hedetniemi, W. Goddard, and P. K. Srimani, A Synchronous Self-stabilizing Minimal Domination Protocol in an Arbitrary Network Graph, IWDC, pp.26-32, 2003.
DOI : 10.1007/978-3-540-24604-6_3

[. Younis, M. Krunz, and S. Ramasubramanian, Node clustering in wireless sensor networks: recent developments and deployment challenges, List of Figures, pp.20-25, 2006.
DOI : 10.1109/MNET.2006.1637928