BOUNDS ON DOUBLE DOMINATION IN SQUARES OF GRAPHS

M. H. Muddebihal, Srinivasa G.

Abstract: Let the square of a graph G , denoted by 2 G has same vertex set as in G and every two vertices u and v are joined in 2 G if and only if they are joined in G by a path of length one or two. A subset D of vertices of 2 G is a double dominating set if every vertex in 2 G is dominated by at least two vertices of D . The minimum cardinality double dominating set of 2 G is the double domination number, and is denoted by ( ) 2 ? d G . In this paper, many bounds on ( ) 2 ? d G were obtained in terms of elements of G . Also their relationship with other domination parameters were obtained.

Keywords: Graph, Square graph, Double dominating set, Double domination number.

DOI: https://doi.org/10.15623/ijret.2013.0209069