"SPLIT AND NON SPLIT TWO DOMINATION NUMBERS OF SEMI TOTAL - POINT GRAPH"

Abstract: A dominating set D ? V of a graph G is a Split two dominating set if the induced subgraph is disconnected and every vertex is adjacent to atleast two vertices in D. The Split two domination number ?s2 (G) is the minimum cardinality of a Split two dominating set. A Dominating set D V of a graph G is a Non Split two dominating set if the induced subgraph is connected and every vertex in V-D is adjacent to atleast two vertices in D. The Non Split two domination number ?ns2 (G) is the minimum cardinality of a Non Split two dominating set. For any graph G = (V, E), the semi total point graph T2(G) = H is the graph whose vertex set is the union of vertices and edges in which two vertices are adjacent if and only if they are adjacent vertices of G or one is a vertex and other is an edge of G incident with it. In this paper we investigate the behavior of Split two and Non Split two domination number for Semi Total – point graphs. Keywords: Split Two Domination Number, Non Split Two Domination Number, & Semi Total - Point Graph.