Xiuying Wang
Abstract
Let G(X,Y;E) be a connected bipartite graph , |X|=|Y|=n,then (1)if NC2=n≥4, then G is vertex—pancyclic bipartite graph. (2)if NC2=n-1≥4,andδ(G)≥2, then G is Hamiltonian, oru∈V(G), G has a C, |C|=2n-2, u∈V(C),and C be domating cycle of G.
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Let G(X,Y;E) be a connected bipartite graph , |X|=|Y|=n,then (1)if NC2=n≥4, then G is vertex—pancyclic bipartite graph. (2)if NC2=n-1≥4,andδ(G)≥2, then G is Hamiltonian, oru∈V(G), G has a C, |C|=2n-2, u∈V(C),and C be domating cycle of G.
Key concepts: Bipartite graph, Combinatorics, Edge-transitive graph, Complete bipartite graph, Mathematics, Pancyclic graph, Graph, Foster graph