Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices

As a real-valued function, a graphical parameter is defined on the class of finite simple graphs, and remains invariant under graph isomorphism. In mathematical chemistry, vertex-degree-based topological indices are the graph parameters of the general form of p_{\phi}(G)=\sum_{uv\in E(G)}\phi(d(u),d(v)), where \phi represents a real-valued symmetric function, and d(u) shows the degree of u\in V(G). In this paper, it is proved that if \phi has certain conditions, then the graph among those with n vertices and m edges, whose difference between the maximum and minimum degrees is at most ۱, has the minimal value of p_{\phi}. Moreover, it is demonstrated that some well-known topological indices are able to satisfy these certain conditions, and the given indices can be treated in a unified manner.

کلیدواژه ها:

Graph parameter ، topological index ، General sum connectivity index ، multiplicative Zagreb indices ، Sombor index ، Forgotten index