Domination for latin square graphs

TL;DR

This paper investigates domination parameters in latin square graphs, providing bounds and explicit formulas for various domination numbers, thereby advancing understanding of their combinatorial properties.

Contribution

It introduces bounds and a formula for domination numbers in latin square graphs, a novel contribution to combinatorial graph theory.

Findings

Bounds for domination and k-tuple total domination numbers

Explicit formula for the 2-tuple total domination number

Enhanced understanding of latin square graph properties

Abstract

In combinatorics, a latin square is a $n\times n$ matrix filled with n different symbols, each occurring exactly once in each row and exactly once in each column. Associated to each latin square, we can define a simple graph called a latin square graph. In this article, we compute lower and upper bounds for the domination number and the k-tuple total domination numbers of such graphs. Moreover, we describe a formula for the 2-tuple total domination number.