Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös,...

Two classes of infinite graphs with unbounded vertex degrees are introduced and studied. These are g-tempered and strongly g-tempered graphs, respectively. In such graphs, the degree growth is controlled by a function g : R+ → R+. It is proven that for g(t) = log t (resp. g(t) = t log t), the number of simple paths of length N originated at a given vertex x (resp. the number of finite connected...

Dvořák et al. introduced a variant of the Randić index of a graph G, denoted by R′(G), where R′(G) = ∑ uv∈E(G) 1 max{d(u),d(v)} , and d(u) denotes the degree of a vertex u in G. The coloring number col(G) of a graph G is the smallest number k for which there exists a linear ordering of the vertices of G such that each vertex is preceded by fewer than k of its neighbors. It is well-known that χ(...

Recently Nikolić, Trinajstić and Randić put forward a novel modification W(G) of the Wiener number W(G), called modified Wiener index , which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as Wmin,λ(G)=∑(V(G) mG(u,ν) −mG(u,ν) ) and show that some of the important properties of W(G), W(G) and W(G) are also properties of...

The sum of the absolute values eigenvalues graph’s adjacency matrix is known as its ordinary energy. Based on a range other graph matrices, several equivalent energies are being considered. In this work, we considered energy, Laplacian, Randi´c, incidence, and Sombor energy to analyze their relationship using polynomial regression. performance each model exceptional with cross-validation RMSE m...

The alternative double bonds and conjugation in the polyene compounds are one of the main properties in these compounds. Each carbon-carbon bonds in a polyene compound along the chain has appreciable double-bond character. The p-electrons are therefore not localized but are relatively free to move throughout the entire carbon skeleton as an one-dimensional box. The skeleton be considered as a r...