On Congruent Domination Number of Disjoint and One Point Union of Graphs

S. K. Vaidya (Department of Mathematics, Saurashtra University, Rajkot, Gujarat(INDIA).)
H. D. Vadhel (Research Scholar, Department of Mathematics, Saurashtra University, Rajkot, Gujarat(INDIA).)

Journal of the Indonesian Mathematical Society
VOLUME 28 NUMBER 3 (NOVEMBER 2022)

A dominating set $D \subseteq V(G)$ is said to be a congruent dominating set of $G$ if $$\sum_{v \in V(G)} d(v) \equiv 0 \left( \bmod\;\sum_{v \in D} d(v)\right).$$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 establish the bounds on congruent domination number in terms of order of disjoint union of graphs as well as one point union of graphs.