Some Upper Bounds on the First General Zagreb Index

The first general Zagreb index M γ G or zeroth-order general Randić index of a graph G is defined as M γ G = ∑ v ∈ V d v γ where γ is any nonzero real number, d v is the degree of the vertex v and γ = 2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth-order general Randić index (for γ < 0 ) in terms of connectivity, minimum degree, and independent number. In this paper, we put sharp upper bounds on the first general Zagreb index in terms of independent number, minimum degree, and connectivity for γ . Furthermore, extremal graphs are also investigated which attained the upper bounds.

General Randić index of unicyclic graphs with given girth and diameter

We study the general Randić index of a graph [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] is the edge set of [Formula: see text] and [Formula: see text] and [Formula: see text] are the degrees of vertices [Formula: see text] and [Formula: see text], respectively. For [Formula: see text], we present lower bounds on the general Randić index for unicyclic graphs of given diameter and girth, and unicyclic graphs of given diameter. Lower bounds on the classical Randić index and the second modified Zagreb index are corollaries of our results on the general Randić index.

Relations between the energy of graphs and other graph parameters

In this paper we give various relations between the energy of graphs and other graph parameters as Randić index, clique number, number of vertices and edges, maximum and minimum degree etc. Moreover, new bounds for the energy of complementary graphs are derived. Our results are based on the concept of vertex energy developed by G. Arizmendi and O. Arizmendi in [Lin. Algebra Appl. doi:10.1016/j.laa.2020.09.025].

Neighborhood-Based Descriptors for Porphyrin Dendrimers

The symmetry of molecular structures is captured by topological indices, which provide a mathematical vocabulary for predicting features such as boiling temperatures, viscosity, and gyration radius and are also employed in QSPR/QSAR research. Dendrimers are a brand-new type of polymer. It is characterized as a macromolecule due to its highly radiated structure, providing great water solubility and adaptability. Because of these features, dendrimers are a strong alternative for medication delivery. This article investigates some topological indices based on neighborhood degrees such as Modified Randic index, Inverse Sum Index, SK, SK1, and SK2 index for some dendrimers.

Several Topological Indices of Two Kinds of Tetrahedral Networks

Tetrahedral network is considered as an effective tool to create the finite element network model of simulation, and many research studies have been investigated. The aim of this paper is to calculate several topological indices of the linear and circle tetrahedral networks. Firstly, the resistance distances of the linear tetrahedral network under different classifications have been calculated. Secondly, according to the above results, two kinds of degree-Kirchhoff indices of the linear tetrahedral network have been achieved. Finally, the exact expressions of Kemeny’s constant, Randic index, and Zagreb index of the linear tetrahedral network have been deduced. By using the same method, the topological indices of circle tetrahedral network have also been obtained.