Dynamics of Boundary Graphs

Authors

  • G. Mariumuthu The Madura College
  • M. S. Saraswathy Thiagarajar College of Engineering

DOI:

https://doi.org/10.3329/jsr.v5i3.14866

Keywords:

Boundary graph, Periodic graph.

Abstract

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)

 

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Author Biographies

G. Mariumuthu, The Madura College

Department of Mathematics, The Madura College, Madurai-625 011

M. S. Saraswathy, Thiagarajar College of Engineering

Department of Mathematics, Thiagarajar College of Engineering, Madurai-625 015

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Published

2013-08-29

How to Cite

Mariumuthu, G., & Saraswathy, M. S. (2013). Dynamics of Boundary Graphs. Journal of Scientific Research, 5(3), 447–455. https://doi.org/10.3329/jsr.v5i3.14866

Issue

Section

Section A: Physical and Mathematical Sciences