On domination number of Latin square graphs of finite cyclic groups

Abstract

This paper aims to find certain bounds for the domination number of Latin square graphs, i.e., a simple graph assigned to a Latin square. In fact, we show that if [Formula: see text] is a Latin square of order [Formula: see text] and [Formula: see text] is the associated Latin square graph of [Formula: see text], then [Formula: see text]. We will investigate in which case the equalities hold. Finally, we study the domination number of Latin square graph associated to groups. In particular, we show that if [Formula: see text], then [Formula: see text]. Also, we prove that if [Formula: see text], then [Formula: see text].

Minimum Dominating Set for the Prism Graph Family

“…In 2021 [11] Liu, Chanjuan discussed about the upper and lower bounds of domination number for n maximal outer planar graph. [5] Bermudo and others proposed some lower bounds on the domination number of a catacondensed hexagonal system using the number of hexagons and the number of branching hexagons [13]. Sarah et al found certain bounds for the domination number of Latin square graphs.…”

Variants of the domination number for flower snarks

“…Other than trivial results such as for paths or cycles, perhaps the most famous result is the sprawling effort over a 27 year period [2,8,14,16,20,36] to provide a complete characterisation of domination numbers for grid graphs G(n, m) of all possible sizes, consisting of 23 special cases before settling into a standard formula for n, m ≥ 16. Other results for domination include generalized Petersen graphs [13,24,41], Cartesian products involving cycles [1,9,28], King graphs [40], Latin square graphs [29], hypercubes [3], Sierpiński graphs [34], Knödel graphs [12], and various graphs from chemistry [26,32], among others.…”

Variants of the Domination Number for Flower Snarks

“…Other than trivial results such as for paths or cycles, perhaps the most famous result is the sprawling effort over a 27 year period [18,14,8,34,2,12] to provide a complete characterisation of domination numbers for grid graphs G(n, m) of all possible sizes, consisting of 23 special cases before settling into a standard formula for n, m ≥ 16. Other results for domination include generalized Petersen graphs [41,23,39], Cartesian products involving cycles [26,9,1], King graphs [40], Latin square graphs [27], hypercubes [3], Sierpiński graphs [32], Knödel graphs [38], and various graphs from chemistry [25,30], among others.…”