M-polynomial and CoM-polynomial of Hat-graphs

Abstract

The M-Polynomial and CoM-polynomial are considered as two of the most important degree-based graph polynomials, since from them we can obtain almost all degree based topological indices and coindices respectively. In this paper these two polynomials will be computed for some new defined graphs from the basic well-known graphs, such graphs will be known as hat-graphs. Hat-graphs have been constructed by adding new vertices and edges for the basic graphs in a special way. The special graphs that have been the base of these new graphs are path, cycle, complete, star, wheel, and complete bipartite graph.