IJPAM: Volume 108, No. 3 (2016)

$T_1$ GRAPHS

Seena V$^1$, Raji Pilakkat$^2$
$^{1,2}$Department of Mathematics
University of Calicut
Calicut University
Malappuram (District), PIN 673 635, Kerala, INDIA


Abstract. A simple graph $G$ is said to be $T_1$ 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 exist two edges $e_1$ and $e_2$ of $G$ such that $e_1$ is incident with $u
$ but not with $v$ and $e_2$ is incident with $v$ but not with $u
$.

In this paper we discuss $T_1$ 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 $T_1$. It proved that line graph of any $T_1$ graph is $T_1$. Moreover, the relations between $T_1$ graphs with its incidence matrix and its adjacency matrix is discussed.

Received: December 4, 2016

AMS Subject Classification: 05C99

Key Words and Phrases: $T_1$ graph, incidence matrix, adjacency matrix, line graph, corona, middle graph

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DOI: 10.12732/ijpam.v108i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 3
Pages: 581 - 589


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