Independent Domination Number for some Special types of Snake Graph

Abstract

Let G(V, E) be a graph, V has a subset C, contains vertices with atleast one vertex in V that is not in C, then G has the dominating set C. If C has vertices that is not adjacent to one another, then G has an independent dominating set C and so the number of vertices present in the set C represents the IDN, the minimum cardinality of the sets C. In this paper, we were going to deal with Snake graphs in specific, Alternate Triangular and Alternate Quadrilateral Snake graphs. Keeping the concepts of these graphs as our base we extend our paper by defining n-Alternative Triangular Snake graphA(Tn), n-Alternative Double Triangular Snake graph nA(D(Tn)), n-Alternative Quadrilateral Snake graphA(Qn) and n-Alternative Double Quadrilateral Snake graphA(D(Qn)). Further we obtain independent domination number for some special types of snake graphs, in particular n-Alternative Triangular Snake graph nA(Tn, n-Alternative Double Triangular Snake graph nA(D(Tn)), n-Alternative Double Triangular Snake graph nA(Qn)and n-Alternative Quadrilateral Snake graph and n-Alternative Double Quadrilateral Snake graphA(D(Qn)).