Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-11-01

Journal: GRAPHS AND COMBINATORICS

Included Journals: Scopus、SCIE

Volume: 31

Issue: 6

Page Number: 2125-2136

ISSN: 0911-0119

Key Words: Vertex pancyclic; Claw-free graph; Quadrangularly connected

Abstract: AgraphG is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of l-cycles (3 <= l <= 4) C-1, C-2,..., C-r such that e1. E(C1), e(2) is an element of E(Cr) and E(C-i) boolean AND E(Ci+1) not equal for i <= 1, 2,..., r -1. In this paper, we show that if G is a quadrangularly connected claw-free graph with d(G) = 5, which does not contain an induced subgraph H isomorphic to either G1 or G2 (where G1, G2 are specified graphs on 8 vertices) such that the neighborhood in G of every vertex of degree 4 in H is disconnected, then G is vertex pancyclic.