International Journal of Mathematics and Soft Computing Vol.6, No.2 (2016), 33 - 41. ISSN Print : 2249 - 3328 ISSN Online : 2319 - 5215 Switching of a vertex and independent domination number in graphs S K Vaidya 1 , R M Pandit 2 1 Department of Mathematics Saurashtra University, Rajkot - 360005 Gujarat, India. samirkvaidya@yahoo.co.in 2 Government Polytechnic Jamnagar - 361009, Gujarat, India. pandit.rajesh@ymail.com Abstract The switching of a vertex v of a graph G means removing all the edges incident to v and adding the edges joining v to every vertex which is not adjacent to v in G.The resultant graph is denoted by  G. In this paper, we explore the concept of independent domination in the context of switching of a vertex in a graph. Keywords: Dominating set, Independent dominating set, Independent domination num- ber, Switching of a vertex. AMS Subject Classification(2010): 05C69; 05C76. 1 Introduction The domination in graphs is one of the concepts in graph theory which has attracted many researchers to work on it because of its many and varied applications in fields like linear alge- bra and optimization, design analysis of communication networks, social sciences and military surveillance. Many variants of domination models are available in the existing literature. For a comprehensive bibliography of papers on the concept of domination, the readers are referred to Hedetniemi and Laskar [9]. This paper is focused on independent domination in graphs. By a graph G we mean a simple, finite and undirected graph G of order n. We denote the vertex set and edge set of a graph G by V (G) and E(G), respectively. The open neighborhood N (v) of v ∈ V (G) is the set of vertices adjacent to v, and the set N [v]= N (v) ∪{v} is the closed neighborhood of v. We denote the degree of a vertex v in a graph G by deg(v). The maximum degree among the vertices of G is denoted by (G). A vertex of degree one is called a pendant vertex and a vertex which is not the end of any edge is called the isolated vertex. The set S ⊆ V (G) of vertices in a graph G is called a dominating set if every vertex v ∈ V (G) is either an element of S or is adjacent to at least one vertex of S . The minimum cardinality of a dominating set in G is called the domination number of G which is denoted by γ (G). 33