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 $G$.