Connected 2-domination polynomials of some graph operations

Abstract

In this paper, we derive the connected 2-domination polynomials of some graph operations. The connected 2-domination polynomial of a graph \(\mathrm{G}\) of order \(m\) is the polynomial \(D_{c 2}(G, x)=\sum_{j=\gamma_{c_2}(G)}^m d_{c 2}(G, j) x^j\), where \(d_{c 2}(G, j)\) is the number of connected 2-dominating sets of \(G\) of size \(j\) and \(\gamma_{c 2}(G)\) is the connected 2-domination number of \(G\).