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In combinatorics, a latin square is a $ntimes n$ 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.
For a graph $G=(V,E)$, we call a subset $ Ssubseteq V cup E$ a total mixed dominating set of $G$ if each element of $V cup E$ is either adjacent or incident to an element of $S$, and the total mixed domination number $gamma_{tm}(G)$ of $G$ is the min
In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph. We also compute the domination number of some families of graphs such as star graphs, double start grap
Given a graph $G$, a dominating set of $G$ is a set $S$ of vertices such that each vertex not in $S$ has a neighbor in $S$. The domination number of $G$, denoted $gamma(G)$, is the minimum size of a dominating set of $G$. The independent domination n
Let $P$ be a partial latin square of prime order $p>7$ consisting of three cyclically generated transversals. Specifically, let $P$ be a partial latin square of the form: [ P={(i,c+i,s+i),(i,c+i,s+i),(i,c+i,s+i)mid 0 leq i< p} ] for some distinct $c,
We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n+O(n/g)<3n/10+O(n/g).