MINIMAL GRAPHS WITH RESPECT TO THE MULTIPLICATIVE VERSION OF SOME VERTEX-DEGREE-BASED TOPOLOGICAL INDICES

Abstract

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-degreebased topological indices are the graph parameters of the general form of (Formula presented.), where ϕ represents a real-valued symmetric function, and d(u) shows the degree of u ∈ V (G). In this paper, it is proved that if ϕ 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 1, has the minimal value of pϕ. 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. © 2025 University of Isfahan