Equitable and Outdegree Equitable Domination in Product Graphs

Thasneem T R; Manju K Menon

doi:10.47000/tjmcs.1785825

Equitable and Outdegree Equitable Domination in Product Graphs

Abstract

An equitable dominating set of a graph $G = (V , E)$, is a subset of vertices $D \subseteq V$ such that each vertex $v\in V-D$, is adjacent to at least one vertex $u\in D$ and the degree of $u$ and $v$ differ by at most 1. The \textbf{equitable domination number} $\gamma^e(G)$ is the size of the smallest equitable dominating set of $G$. For a vertex $u$ in the dominating set $D$ of a graph $G$, the number of edges from $u$ to $V-D$ is called the outdegree of $u$ with respect to $D$, $d_{D, G}^o(u)$. A dominating set $D$ is called the outdegree equitable dominating set if the absolute value of the differences of outdegrees of any two vertices in $D$ is at most one. The \textbf{outdegree equitable domination number} of $G$ $\gamma_{oe}(G)$ is the size of the smallest outdegree equitable dominating set of $G$. In this paper equitability related domination parameters such as equitable domination number and outdegree equitable domination number are analyzed within the realm of some graph products specifically the cartesian and the strong product of graphs.

Keywords

Supporting Institution

St. Paul's College, Kalamassery, Kerala, India

Project Number

1785825-AF-T0-V0-20250917114435

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Thasneem T R ^*
0000-0001-5189-8648
India

Manju K Menon This is me
0000-0002-5692-825X
India

Publication Date

October 13, 2026

Submission Date

September 27, 2025

Acceptance Date

March 27, 2026

Published in Issue

Year 2026 Volume: 18 Number: 3

DOI

https://doi.org/10.47000/tjmcs.1785825

IZ

https://izlik.org/JA38TK56DW

Cite

RIS / Bibtex

APA

T R, T., & Menon, M. K. (2026). Equitable and Outdegree Equitable Domination in Product Graphs. Turkish Journal of Mathematics and Computer Science, 18(3), 893-902. https://doi.org/10.47000/tjmcs.1785825

AMA

1.T R T, Menon MK. Equitable and Outdegree Equitable Domination in Product Graphs. TJMCS. 2026;18(3):893-902. doi:10.47000/tjmcs.1785825

Chicago

T R, Thasneem, and Manju K Menon. 2026. “Equitable and Outdegree Equitable Domination in Product Graphs”. Turkish Journal of Mathematics and Computer Science 18 (3): 893-902. https://doi.org/10.47000/tjmcs.1785825.

EndNote

T R T, Menon MK (October 1, 2026) Equitable and Outdegree Equitable Domination in Product Graphs. Turkish Journal of Mathematics and Computer Science 18 3 893–902.

IEEE

[1]T. T R and M. K. Menon, “Equitable and Outdegree Equitable Domination in Product Graphs”, TJMCS, vol. 18, no. 3, pp. 893–902, Oct. 2026, doi: 10.47000/tjmcs.1785825.

ISNAD

T R, Thasneem - Menon, Manju K. “Equitable and Outdegree Equitable Domination in Product Graphs”. Turkish Journal of Mathematics and Computer Science 18/3 (October 1, 2026): 893-902. https://doi.org/10.47000/tjmcs.1785825.

JAMA

1.T R T, Menon MK. Equitable and Outdegree Equitable Domination in Product Graphs. TJMCS. 2026;18:893–902.

MLA

T R, Thasneem, and Manju K Menon. “Equitable and Outdegree Equitable Domination in Product Graphs”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 3, Oct. 2026, pp. 893-02, doi:10.47000/tjmcs.1785825.

Vancouver

1.Thasneem T R, Manju K Menon. Equitable and Outdegree Equitable Domination in Product Graphs. TJMCS. 2026 Oct. 1;18(3):893-902. doi:10.47000/tjmcs.1785825