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

S. K. Vaidya; H. D. Vadhel

doi:10.22342/jims.28.3.1102.251-258

S. K. Vaidya ⁽¹⁾ , H. D. Vadhel ⁽²⁾

(1) Department of Mathematics, Saurashtra University, Rajkot, Gujarat(INDIA)., India,

(2) Research Scholar, Department of Mathematics, Saurashtra University, Rajkot, Gujarat(INDIA)., India

https://doi.org/10.22342/jims.28.3.1102.251-258

Issue
VOLUME 28 NUMBER 3 (NOVEMBER 2022)

Submitted
November 23, 2021

Accepted
November 28, 2022

Published
November 30, 2022

Keywords:

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

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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.

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Authors

S. K. Vaidya

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

http://orcid.org/0000-0002-5394-1424

samirkvaidya@yahoo.co.in (Primary Contact)

H. D. Vadhel

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

http://orcid.org/0000-0003-0890-738X

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).

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