Abstract. A simple graph $G$ is said to be $T_0$ if for any two distinct vertices $u
$ and $v$ of $G$, one of the following conditions hold:
  1. At least one of $u
$ and $v$ is isolated;
  2. There exists an edge $e$ such that either $e$ is incident with $u
$ but not with $v$ or $e$ is incident with $v$ but not with $u

In this paper we discuss $T_0$ graphs and some examples of it. This paper also deals with the sufficient conditions for join of two graphs, middle graph of a graph and corona of two graphs to be $T_0$. It is established via example that the line graph of a $T_0$ graph need not be $T_0$. Moreover, the relations between $T_0$ graph with its incidence matrix and its adjacency matrix is discussed.

AMS Subject Classification: 05C99

Download full article from here (pdf format).

DOI: 10.12732/ijam.v29i1.11

Volume: 29
Issue: 1
Year: 2016