On the doubly connected domination polynomial of a graph

Abstract

© 2019 World Scientific Publishing Company Let (Formula presented.) be a simple graph. A set (Formula presented.) is a doubly connected dominating set of (Formula presented.) if it is a dominating set and both induced subgraphs (Formula presented.) and (Formula presented.) are connected. In this paper, we introduce the doubly connected domination polynomial of a graph. We investigate some properties of these polynomials for some specific graphs. Also, we compute the doubly connected domination polynomial for some families of graphs such as the friendship graphs and the cactus chains graphs.