【摘要】In1989,Zhu,LiandDengintroducedthedefinitionofimplicitdegreeofavertexvinagraphG,denotedbyid(v).Inthispaper,weprovethatifGisa2-connectedgraphofordernsuchthatid(u)+id(v)≥nforeachpairofnonadjacentverticesuandvinG,thenGispancyclicunlessGisbipartite,orelsen=4r,r≥2andGisisomorphictoF4r.
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