Domination Parameters Of Star Graph

The \(n\)-star graph \(S_n\) is a simple graph whose vertex set is the set of all \(n!\) permutations of \(\{1,2,\ldots,n\}\) and two vertices \(\alpha\) and \(\beta\) are adjacent if and only if \(\alpha(1) \neq \beta(1)\) and \(\alpha(i) \neq \beta(i)\) for exactly one \(i\), \(i \neq 1\). In the paper, we determine the values of the domination number \(\gamma\), the independent domination number \(\gamma_i\), the perfect domination number \(\gamma_p\), and we obtain bounds for the total domination number \(\gamma_t\) and the connected domination number \(\gamma_c\) for \(S_n\).