Resolving Domination Numbers of Family of Tree Graph

Abstract

All graph in this paper are members of family of graph tree. Let G is a connected graph, for an ordered set W={w1,w2,...,wk} of vertices and a vertex which is not element of W, then W is dominating set of graph G when the vertices that are not listed at W are vertices which are adjacent with W. The minimum cardinality of dominating set of graph G is called dominating numbers denoted  G  . If W and a vertex on graph G are connected each other, the metric representation of v which is element of W is the k-vector r(v|W)=(d(v,w1), d(v,w2),..., d(v,wk)), where d(x,y) represents distance between x and y. Then, W is resolving dominating set of graph G if the distance of all vertices is different respect to W. The minimum cardinality of resolving dominating set is called resolving domination numbers denoted (G ) r . In this paper we found the exact values of resolving dominating for firecracker graph, caterpillar graph and banana tree graph.