科研之友
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摘要
Zhu, Li and Deng introduced in 1989 the definition of implicit degree of a vertex v in a graph G, denoted by id(v), by using the degrees of the vertices in its neighborhood and the second neighborhood. And they obtained sufficient conditions with implicit degrees for a graph to be hamiltonian. In this paper, we prove that if G is a 2-connected graph of order n a parts per thousand yen 3 such that id(v) a parts per thousand yen n/2 for each vertex v of G, then G is pancyclic unless G is bipartite, or else n = 4r, r a parts per thousand yen 2 and G is in a class of graphs F (4r) defined in the paper.
