• CONNECTED ROMAN BLOCK DOMINATION IN GRAPHS

Abstract

A Roman dominating function (RDF) on a block graph B(G) = (H, X) is defined as a function f: H® {0, 1, 2} satisfying  the  condition  that  every  vertex u for  which f(u) = 0  is  adjacent  to  at  least  one  vertex v for  which f (v) = 2. The  weight  of  a  Roman  dominating function  of B(G)  is  defined  as . The  Roman  domination  number  of  a  block graph B(G)  is  denoted  by , equals  the  minimum  weight  of  a  RDF of B(G). A Roman dominating function of B(G) is connected Roman dominating function of B(G) if either or is  connected. The  connected Roman  block  domination  number is  the  minimum  weight  of  a  connected  Roman  block  dominating function of B(G). In  this  paper we establish  some  results on in terms  of  elements  of G. Further we develop its relationship with other different dominating parameters.