IJPAM: Volume 87, No. 3 (2013)

$\gamma $-STABLE TREE

M. Yamuna$^1$, K. Karthika$^2$
SAS, VIT University
Vellore, Tamilnadu, INDIA

Abstract. For a given non-adjacent pair $\{ x, y \}$ in a graph $G$, we denote by $G_{xy}$ the graph obtained by deleting $x$ and $y$ and adding a new vertex $xy$ adjacent to precisely those vertices of $G - x - y$ which were adjacent to at least one of $x$ or $y$ in $G$. We say that $G_{xy}$ is obtained by contracting on $\{ x, y \}$. In this paper we introduce $\gamma $-stable graphs and we have established that $\gamma $-stable trees have a unique structure.

Received: June 30, 2013

AMS Subject Classification: 05C69

Key Words and Phrases: domination, $\gamma $-stable

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DOI: 10.12732/ijpam.v87i3.9 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 3