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An implicit degree ore-condition for pancyclicity of graphs |
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| Authors: | Hao Li Jun Qing Cai |
| Institution: | 1. L.R.I, UMR 8623, CNRS and Université Paris-Sud 11, F-91405, Orsay, France 2. Institute for Interdisciplinary Research, Jianghan University, Wuhan, 430019, P. R. China 3. School of Management, Qufu Normal University, Rizhao, 276826, P. R. China |
| Abstract: | In 1989, Zhu, Li and Deng introduced the definition of implicit degree of a vertex v in a graph G, denoted by id(v). In this paper, we prove that if G is a 2-connected graph of order n such that id(u)+id(v) ≥ n for each pair of nonadjacent vertices u and v in G, then G is pancyclic unless G is bipartite, or else n = 4r, r ≥ 2 and G is isomorphic to F 4r . |
| Keywords: | Implicit degree Hamilton cycle pancyclic graph |
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