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GLOBAL EQUITABLE DOMINATION IN CARTESIAN PRODUCT OF GRAPHS
Keywords:
global dominating set, equitable dominating set, global equitable dominating set, global equitable domination number, Cartesian productDOI:
https://doi.org/10.17654/0974165824025Abstract
The most famous open problem involving domination in graphs is Vizing's conjecture which states that the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. In this paper, we investigate a similar problem for global equitable domination. In particular, we explore the multiplicative nature of the global equitable domination number $\left(\gamma_g^e\right)$ on the Cartesian products $P_n \square P_2, C_n \square P_2$ and $C_n \square K_m$.
Received: April 19, 2024
Revised: May 10, 2024
Accepted: May 29, 2024
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