SUPERLATIVE TOTAL DOMINATION IN GRAPHS

. Let G = ( V,E ) be a simple graph with no isolated vertices and p ≥ 3. A set D ⊆ V is a dominating set, abbreviated as DS , of a graph G , if every vertex in V − D is adjacent to some vertex in D , while a total dominating set, abbreviated as TDS , of G is a set T ⊆ V such that every vertex in G is adjacent to a vertices in T . A set T is a superlative total dominating set, abbreviated as STDS , of G if V − T is not contains a TDS but it contains a DS of G . The superlative total domination number γ st ( G ) is the minimum cardinality of a STDS of G . In this paper, we initiate a study on γ st ( G ) and its exact values for some classes of graphs. Furthermore, bounds in terms of order, size, degree and other domination related parameters are investigated.