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A graph G is triangularly connected if for every pair of edges e 1 , e 2 ∈ E(G), G has a sequence of 3-cycles C 1 , C 2 , · · · , C l such that e 1 ∈ C 1 , e 2 ∈ C l and such that E(C i) ∩ E(C i+1) = ∅, (1 ≤ i ≤ l − 1). In this paper it is shown that every triangularly connected claw-free graph G with |E(G)| ≥ 3 is vertex pancyclic. This implies the former(More)
In this paper we develop the technique of a distribution decomposition for a graph. A formula is given to determine genus distribution of a cubic graph. Given any connected graph, it is proved that its genus distribution is the sum of those for some cubic graphs by using the technique. We consider finite connected graphs. Surfaces are orientable(More)
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