• TOTAL EFFICIENT DOMINATION IN GRAPHS

Abstract

A set D of vertices of a graph G is a total efficient dominating set if every vertex in V is adjacent to exactly one vertex in D. The total efficient domination number g_te(G) of G is the minimum cardinality of a total efficient dominating set of G. In this paper, the exact values of g_te(G) for some standard graphs are found and some bounds are obtained. Also a Nordhaus-Gaddum type result is established. In addition, the total efficient domatic number d_te(G) of G is defined to be maximum order of a partition of the vertex set of G into total efficient dominating sets of G. Also a relation between g_te(G) and d_te(G) is established.