Abstract

The aim of this paper is to study about the number of cc-dominating sets and to introduce the concept of \textit{cc-domination polynomial} for simple finite undirected graphs. For a graph $G$ on $n$ vertices possessing $d_{c}(G,i)$ cc-dominating sets of cardinality $i$, the \textit{cc-domination polynomial} is defined as $D_{c}[G;x] =\sum_{i=\gamma_{cc}(G)}^{n}$ $d_{c}(G, i)x^i$, where $\gamma_{cc}(G)$ is the cc-domination number of $G$. We obtain some properties of $D_{c}[G; x]$ and compute the same for some special graphs. Moreover, the concept of cc-domination entropy is also introduced and studied.

Keywords and Phrases

CC-Domination Polynomial, CC-Domination Number, Closely-connected Vertices, CC-Degree of a Vertex, CC-Isolated Vertex, CC-Domination Entropy.

A.M.S. subject classification

05C40, 05C69, 05A18.

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