BLOCK DOUBLE DOMINATION IN GRAPHS

Abstract

For any graph , the block graph  of a graph  is the graph whose set of vertices is the union of the set of blocks of  in which two vertices are adjacent if and only if the corresponding blocks of  are adjacent. A subset  of  is double dominating set of  if for every vertex  that is  is in  and has at least one neighbour in  or  is in  and has at least two neighbours in  The block double dominating number  is a minimum cardinality of block double dominating set. In this paper, we establish upper and lower bounds on  in terms of elements of  and other dominating parameters of  are obtained.