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Submitted
November 23, 2021
Accepted
November 28, 2022
Published
November 30, 2022
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Abstract

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.

Keywords

Dominating Set Domination Number Congruent Dominating Set Congruent Domination Number

Article Details

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author Biographies

S. K. Vaidya, Department of Mathematics, Saurashtra University, Rajkot, Gujarat(INDIA).

Professor & Head,

Department of Mathematics,

Saurashtra University, Rajkot, Gujrat(INDIA).

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

Research Scholar,
Department of Mathematics,
Saurashtra University, Rajkot, Gujarat(INDIA).
How to Cite
Vaidya, S. K., & Vadhel, H. D. (2022). On Congruent Domination Number of Disjoint and One Point Union of Graphs. Journal of the Indonesian Mathematical Society, 28(3), 251–258. https://doi.org/10.22342/jims.28.3.1102.251-258
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