Journal of Algorithms and Computation

This paper is about producing a new kind of pairs which we call MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present some applications of these pairs that show their interesting properties ... Read More

Some new results on the number of fair dominating sets

Saeid Alikhani; Davood Bakhshesh; Nasrin Jafari; Maryam Safazadeh

Volume 54, Issue 2 , December 2022, , Pages 1-12

https://doi.org/10.22059/jac.2022.90381

Abstract

Let $G=(V, E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of the smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair ... Read More

Journal of Algorithms and Computation

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Author = Saeid Alikhani

Sequence pairs related to produced graphs from a method for dividing a natural number by two.

Abstract

Some new results on the number of fair dominating sets

Abstract