$T_0$ GRAPHS
Seena V1, Raji Pilakkat2
1,2Department of Mathematics
University of Calicut
Malappuram (District), PIN 673 635, Kerala, INDIA
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
Key Words and Phrases: $T_0$ graph, incidence matrix, adjacency matrix, line graph, corona, middle graph


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DOI: 10.12732/ijam.v29i1.11

Volume: 29
Issue: 1
Year: 2016