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- W2587433615 abstract "Let G be a 2-connected graph of order n. For any u ∈ V (G) and l ∈ {m,m + 1,...,n}, if G has a cycle of length l, then G is called [m,n]pancyclic, and if G has a cycle of length l which contains u, then G is called [m,n]-vertex pancyclic. Let �(G) be a minimum degree of G and let NG(x) be the neighborhood of a vertex x in G. In [Australas. J. Combin. 12 (1995), 81–91] Liu, Lou and Zhao proved that if |NG(u) ∪ NG(v)| + �(G) ≥ n+1 for any nonadjacent vertices u,v of G, then G is [3,n]-vertex pancyclic. In this paper, we prove if n ≥ 6 and |NG(u)∪NG(v)|+dG(w) ≥ n for every triple independent vertices u,v,w of G, then (i) G is [3,n]pancyclic or isomorphic to the complete bipartite graph Kn/2,n/2, and (ii) G is [5,n]-vertex pancyclic or isomorphic to the complete bipartite graph Kn/2,n/2." @default.
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- W2587433615 date "2008-02-01" @default.
- W2587433615 modified "2023-09-26" @default.
- W2587433615 title "A neighborhood and degree condition for pancyclicity and vertex pancyclicity" @default.
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