# Independent transversal domination subdivision number of trees

Document Type : Original paper

Authors

1 Department of Mathematics, D.B. Jain College, Chennai 600 097, Tamil Nadu, India

2 Department of Mathematics, S.D.N.B. Vaishnav College for Women, Chennai 600 044, Tamil Nadu, India

Abstract

A set $S\subseteq V$ of vertices in a graph $G=(V,E)$ is called a dominating set if every vertex in $V \setminus S$ is adjacent to a vertex in S. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. The domination subdivision number $sd_{\gamma}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the domination number. Sahul Hamid  defined a dominating set which intersects every maximum independent set in $G$ to be an \textit{independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number} of $G$ and is denoted by $\gamma_{it}(G)$. We extend the idea of domination subdivision number  to independent transversal domination.  The independent transversal domination subdivision number of a graph $G$ denoted by $sd_{\gamma_{it}}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the independent transversal domination number. In this paper we initiate a study of this parameter with respect to trees.

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