无爪图中子图的度和与Hamilton连通性.pdfVIP

Advances in Applied Mathematics 应用数学进展, 2014, 3, 8-16 /10.12677/aam.2014.31002 Published Online February 2014 (/journal/aam.html) The Hamilton-Connectivity with the Sum Degree of Subgraph in Claw-Free Graphs Jing Mi, Jianglu Wang School of Mathematical Sciences, Shandong Normal University, Jinan Email: 751374463@ th th rd Received: Dec. 19 , 2013; revised: Jan. 16 , 2014; accepted: Feb. 3 , 2014 Copyright © 2014 Jing Mi, Jianglu Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for Hans and the owner of the intellectual property Jing Mi, Jianglu Wang. All Copyright © 2014 are guarded by law and by Hans as a guardian. Abstract: In this paper, we defined the degree of subgraph, and got the following result on the basis of the degree of subgraph: Let G be a 2-connected claw-free graph of order n, δ G ≥3 . If H and H , any two ( ) 1 2 non-adjacent subgraphs, are isomorphic to P and K , respectively, and d(H ) + d(H ) ≥n, for each pair of u,v 3 2 1 2 ∈G, when {u,v} isn’t a cut set, there exists a Hamilton-path in u,v. Keywords: Claw-Free Graph; Non-Adjacent Subgraph; Degree of Subgraph; Hamilton-Path 无爪图中子图的度和与Hamilton 连通性