Graphs with equal Grundy domination and independence number

The Grundy domination number, γgr(G), of a graph G is the maximum length sequence (v1,v2,…,vk) vertices in such that for every i∈{2,…,k}, closed neighborhood N[vi] contains vertex does not belong to any N[vj], where j<i. It well known number greater than or equal upper Γ(G), which turn independence α(G). In this paper, we initiate study class graphs with Γ(G)=γgr(G) and its subclass consisting α(G)=γgr(G). We characterize latter among all twin-free connected graphs, provide properties these prove hypercubes are members class. addition, give several necessary conditions present large families graphs.