Line graphs of monogenic semigroup graphs (Q2035709)

Summary: The concept of monogenic semigroup graphs \(\Gamma (\mathcal{S}_M)\) is firstly introduced by \textit{K. Ch. Das} et al. [J. Inequal. Appl. 2013, Paper No. 44, 13 p. (2013; Zbl 1283.05067)] based on zero divisor graphs. In this study, we mainly discuss the some graph properties over the line graph \(L (\Gamma (\mathcal{S}_M))\) of \(\Gamma (\mathcal{S}_M)\). In detail, we prove the existence of graph parameters, namely, radius, diameter, girth, maximum degree, minimum degree, chromatic number, clique number, and domination number over \(L (\Gamma (\mathcal{S}_M))\).