International Journal of Engineering, Science and
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<b>ECCENTRIC DOMINATION IN TOTAL GRAPH OF A GRAPH</b>
M. Bhanumathi1,R. M. Mariselvi2
Let G be a simple graph with vertex set V(G) and edge set E(G). The total graph T(G) of G is a graph with vertex set V(G) ? E(G) where two vertices are adjacent if and only if they are adjacent vertices of G or they are adjacent lines of G or one is a vertex of G and another is a line of G incident with it.
8-17
Volume 6, Issue 6
October 2017
Let G be a simple graph with vertex set V(G) and edge set E(G). The total graph T(G) of G is a graph with vertex set V(G) ? E(G) where two vertices are adjacent if and only if they are adjacent vertices of G or they are adjacent lines of G or one is a vertex of G and another is a line of G incident with it. In this paper we studied the concept of eccentric domination number of total graph T(G), obtained bounds of this parameter and determined its exact value for several classes of graphs. Keywords: Eccentric domination number, Total graph.