### Connected domination value in graphs

#### Abstract

In a connected graph *G* = (*V,E*), a set *D* ⊂ *V* is a *connected dominating set* if for every vertex *v* ∈ *V *\ *D*, there exists *u* ∈ *D* such that *u* and *v* are adjacent, and the subgraph〈*D*〉induced by *D* in *G* is connected. A connected dominating set of minimum cardinality is called a *γ _{c}*-set of

*G*. For each vertex

*v*∈

*V*, we define the

*connected domination value*of

*v*to be the number of

*γ*-sets of

_{c}*G*to which

*v*belongs. In this paper, we study the properties of connected domination value of a connected graph

*G*and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of

*γ*-sets for a few well-known family of graphs.

_{c}#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.11

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