Abstract

A dominating set $D \subseteq V(G)$ is said to be a congruent dominating set(CDS) of $G$ if $$\sum_{v \in V(G)} d(v) \equiv 0 \left( \bmod\;\sum_{v \in D} d(v)\right)$$

\par The minimum cardinality of a minimal congruent dominating set of $G$ is called the congruent domination number of $G$ which is denoted by $\gamma_{cd}(G)$. We investigate congruent domination number of some cycle related graphs. 

Keywords and Phrases

Dominating Set, Domination Number, Congruent Dominating Set, Congruent Domination Number.

A.M.S. subject classification

05C07, 05C69.

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