| Summary: | <p class="p1">In a connected graph <em>G</em> = (<em>V,E</em>), a set <em>D</em> ⊂ <em>V</em> is a <em>connected dominating set</em> if for every vertex <em>v</em> ∈ <em>V </em>\ <em>D</em>, there exists <em>u</em> ∈ <em>D</em> such that <em>u</em> and <em>v</em> are adjacent, and the subgraph〈<em>D</em>〉induced by <em>D</em> in <em>G</em> is connected. A connected dominating set of minimum cardinality is called a <em>γ<sub>c</sub></em>-set of <em>G</em>. For each vertex <em>v</em> ∈ <em>V</em>, we define the <em>connected domination value</em> of <em>v</em> to be the number of <em>γ<sub>c</sub></em>-sets of <em>G</em> to which <em>v</em> belongs. In this paper, we study the properties of connected domination value of a connected graph <em>G</em> and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of <em>γ<sub>c</sub></em>-sets for a few well-known family of graphs.</p>
|
|---|