Abstract
Dominating set is a set D of vertices of graph G(V, E) and every vertex u ∈ V(G) − D is adjacent to some vertex υ ∈ D. The set D is called independent set if no two vertices in D are adjacent. Independent domination number of G is the minimum cardinality of D and denoted by γi(G). The metric representation of vertex υ in connected graph G with respect to an ordered set W = w1,w2,w3,...,wk of vertices is the k-vector r(υ|W) = (d(υ|w1), d(υ|w2), d(υ|w3),..., d(υ|wk)), where d(υ, w) represents the distance between the vertices υ and w. The set W is resolving independent dominating set for G if W is independent in G, and distinct vertices of G have distinct representations with respect to W. The minimum cardinality of resolving independent dominating set is called resolving independent domination number and denoted by γri(G). In this paper, we analyze the resolving independent domination number of path graph, cycle graph, friendship graph, helm graph, and fan graph.
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