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In 1997 Bollobás and Thomason (J. Graph Theory 26:165–173, 1997) and Brandt (Discrete Appl. Math. 79:63–66, 1997) defined the weakly pancyclic. In this paper we define weakly vertex-pancyclic and obtain a new sufficient condition for graph to be weakly vertex-pancyclic as the following: if G is a 2-connected graph of order n, and $\{|N(u)\cup N(v)|+d(w):u,v,w\in V(G),uv\not\in E(G)$ , wu, or $wv\not\in E(G)\}\geq n+1$ , then G is weakly vertex-pancyclic. This result also implies a conjecture of Faudree et al.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2008
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