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Abstract
Let the square of a graphG , 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.
Key words: Graph, Square graph, Double dominating set, Double domination number.
Subject Classification Number: AMS05C69, 05C70.
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