Result on The Weak Non-Split Independent Domination Number of Some Special Graphs

Abstract

A graph   has a vertex set  and edge set  and  .  A non - empty subset D is an independent dominating set if every vertex in     is adjacent a vertex in  and   is a non – adjacent vertices. The domination number is the minimum cardinality of an independent dominating set. If, in addition let  and  be the element of .  Then  weakly dominates  if  (i)  and (ii) . A set S is a weak non-split dominating set of  if every vertex is   is weakly dominated by at least one vertex in  and the induced subgraph  is connected. The minimum cardinality of a weak non-split independent dominating set is the weak non-split independent domination number of  G .The  main purpose of this paper is to introduce the concept of weak non-split independent domination number.  For that  we have chosen Soifer graph, Chvatal graph, Fritsch graph, Herschel graph, Moser graph, Franklin graph to find the weak non-split domination number.