【摘 要】
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A graph G is called pancyclic if it contains cycles of length 1, for each 3 ≤ l ≤ n.In 1989, Zhu, Li and Deng introduced the definition of implicit degrees of
【机 构】
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SchoolofMathematicsandInformationScience,HenanPolytechnicUniversity
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A graph G is called pancyclic if it contains cycles of length 1, for each 3 ≤ l ≤ n.In 1989, Zhu, Li and Deng introduced the definition of implicit degrees 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 ≥ 3 such that id(v) ≥ n/2 for each vertex v of G, then G is pancyclic unless G is bipartite, or else n =4r, r ≥ 2 and G is in a class of graphs F4r.
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