On domination and independent domination numbers of a graph

Abstract

For a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:. Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G). Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends the result γ(L(T))=i(L(T)), where T is a tree. Hedetniemi and Mitchell, S. E. Conf. Baton Rouge, 1977.). Corollary 2. For any Graph G, γ(M(G))=i(M(G)), where M is the middle graph of G. © 1978.