文章基本信息

标题：Dynamics of Boundary Graphs
其他标题：Dynamics of Boundary Graphs
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作者：G. Mariumuthu ; M. S. Saraswathy
期刊名称：Journal of Scientific Research
印刷版ISSN：2070-0237
电子版ISSN：2070-0245
出版年度：2013
卷号：5
期号：3
页码：447-455
DOI：10.3329/jsr.v5i3.14866
语种：English
出版社：Rajshahi University
摘要：In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. A vertex v is a boundary vertex of a vertex u if for all The boundary graph B(G) based on a connected graph G is a simple graph which has the vertex set as in G. Two vertices u and v are adjacent in B(G) if either u is a boundary of v or v is a boundary of u. If G is disconnected, then each vertex in a component is adjacent to all other vertices in the other components and is adjacent to all of its boundary vertices within the component. Given a positive integer m, the mth iterated boundary graph of G is defined as A graph G is periodic if for some m. A graph G is said to be an eventually periodic graph if there exist positive integers m and k >0 such that We give the necessary and sufficient condition for a graph to be eventually periodic. Keywords: Boundary graph; Periodic graph. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v5i3.14866 J. Sci. Res. 5 (3), xxx-xxx (2013)
关键词：Mathematics;Boundary graph; Periodic graph.