On the Domination Number of the Circulant Graphs \(C(n; {1,2}), C(n; {1,3})\) and \(C(n; {1, 4})\)

Abstract

Let \(G = (V(G), E(G))\) be a graph. A set \(S \subseteq V(G)\) is a dominating set if every vertex of \(V(G) – S\) is adjacent to some vertices in \(S\). The domination number \(\gamma(G)\) of \(G\) is the minimum cardinality of a dominating set of \(G\). In this paper, we study the domination number of the circulant graphs \(C(n; \{1, 2\})\), \(C(n; \{1, 3\})\), and \(C(n; \{1, 4\})\) and determine their exact values.