The variable sum exdeg index of a graph G is defined as $SEI_a(G)=sum_{uin V(G)}d_G(u)a^{d_G(u)}$, where $aneq 1$ is a positive real number,  du(u) is the degree of a vertex u ∈ V (G). In this paper, we characterize the graphs with the extremum variable sum exdeg index among all the graphs having a fixed number of vertices and cut edges, for every a>1.

Recently, discrete and variable Adriatic indices have been introduced and it has been shown that the sum α -exdeg index is good predictor (when variable parameter is equal to 0.37 ) of the octanol-water partition coefficient for octane isomers. Here, we study mathematical properties of this descriptor. Namely, we analyze extremal graphs of this descriptor in the following classes: the class of ...

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...

Abstract We consider two recent conjectures made by Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index exclusive number of graphs. One conjecture posits an exact relationship first invariants; we show that in fact predicted value may be arbitrarily far from truth either direction. In process establish some new bounds on both...

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...