The theory of combinatorial maps and its use in the graph-topological computations.

Dainis Zeps (1)

1 IMCS - Institute of Mathematics and Computer Science

In this work we investigate combinatorial maps coded via permutations, applying the geometrical idea of considering the corners between the edges in the embedding of the graph on the surface to be the elements on which the permutations act. Combinatorial maps as well partial combinatorial maps are considered, theory of cycle covers, that give objects that correspond to the cycles in the graphs, are developed. Some formulae in permutations are found that calculate useful characteristics of maps. General idea of the work is to find useful applications: finding some quantities computable in permutations that has graph-theoretical characteristics in correspondence. The computer program is implemented that computes the formulae and algorithms obtained from the developed theory.

Šajā darbā mēs pētam kombinatoriskās kartes, kas tiek kodētas kā permutāciju pāri, pielietojot ģeometrisku ideju, ka stūri starp šķautnēm grafam, kas izvietots uz virsmas, ir elementi, uz kuriem permutācijas darbojas.
Ģeometriskās kombinatoriskās kartes kā arī parciālās kartes tiek aplūkotas, ciklu pārklājumu teorija, kas dod objektus, kas atbilst cikliem grafā, tiek attīstīta. Tiek atrastas dažas permutāciju formulas, kas rēķina grafu teorētiskos pielietojumos aktuālus karšu raksturlielumus. Visa darba ideja ir meklēt noderīgus pielietojumus: atrast permutāciju izteiksmēs rēķināmus raksturlielumus, kuriem atbilst grafu teorētiski raksturlielumi.
Datorprograma, kas rēķina permutāciju formulas un no attīstītās teorijas iegūtos algoritmus, ir izveidota.

Mots clés: combinatorics; combinatorial maps; permutations; rotations in graphs; graph topology; graph topological algorithms

Domaines: Mathématiques [math]

Dainis Zeps. The theory of combinatorial maps and its use in the graph-topological computations.. Mathematics [math]. Institute of Mathematics and Computer Science. University of Latvia, 1998. English. ⟨NNT : ⟩. ⟨tel-00417773⟩