Some Indices over a New Algebraic Graph

Abstract

In this paper, we first introduce a new graph $\mathrm{\Gamma }\left(\mathcal{N}\right)$ over an extension $\mathcal{N}$ of semigroups and after that we study and characterize the spectral properties such as the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index, and also perfectness for $\mathrm{\Gamma }\left(\mathcal{N}\right)$ . Moreover, we state and prove some important known Zagreb indices on this new graph.