An Alexandroff topology on graphs

Document Type : Research Paper

Authors

1 Zanjan University

2 Ferdowsi University of Mashhad

3 Zanjan University, Zanjan

Abstract

Let G = (V,E) be a locally finite graph, i.e. a graph in which
every vertex has finitely many adjacent vertices. In this paper, we
associate a topology to G, called graphic topology of G and we show
that it is an Alexandroff topology, i.e. a topology in which intersec-
tion of every family of open sets is open. Then we investigate some
properties of this topology. Our motivation is to give an elementary
step toward investigation of some properties of locally finite graphs
by their corresponding topology which we introduce in this paper.

Keywords

Main Subjects


Volume 39, Issue 4 - Serial Number 4
September 2013
Pages 647-662
  • Receive Date: 24 October 2010
  • Revise Date: 30 May 2011
  • Accept Date: 30 May 2011
  • First Publish Date: 01 September 2013