Mev-polynomial and K Banhatti Indices of Some Hat-graphs - Karim, Akar H.; Ramadan, Ayad M. (Jambura Journal of Mathematics, 2026)
A graph polynomial that has taken several attentions is M-polynomial due to it's significant a considerable number of studies have been conducting on it, moreover some other versions of this polynomial have been defined. In this paper an new version of M-polynomial is presented that will be known as Mve-Polynomial which is an extension of the notation of M-polynomial for comparison between vertices and corresponding adjacent edges. Then we investigate the mathematical relationship between Mve-Polynomial and two resent defined topological indices: first and second K Banhatti indices. Next, we establish explicit formulas for the Mve-Polynomial of some graphs in the family of hat-graphs with it's plots for special number of vertices. From these results we further deduce the corresponding K Banhatti indices.