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.

M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.

Analysis of COVID-19 by Means of Graph Theory

As a powerful displaying, investigation and computational device, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graphs can communicate the sub-atomic structure. Where cell, quality or protein can be indicated as a vertex, and the associate component can be viewed as an edge. Thusly, the biological activity characteristic can be measured via topological index computing in the comparing graphs. In this article, we for the most part concentrate some topological lists for the Corona virus graph. At first,we give a general type of M-polynomial. From the M-polynomial, we recoup some well-known degree-based topological lists, for example, First and Second Zagreb Indices, Second Modified Zagreb Index, Randic´ Index, General Randic´ Index, Symmetric Division Index, Harmonic Index, Inverse Sum Index, Augmented Zagreb Index. Our results are extensions of many existing results.

Топологические аспекты триангулярных борных нанотрубок и альфа-борных нанотрубок

Topological graph indices have been used in a lot of areas to study required properties of different objects such as atoms and molecules. Such indices have been described and studied by many mathematicians and chemists since most graphs are generated from molecules by replacing each atom with a vertex and each chemical bond with an edge. These indices are also topological graph invariants measuring several chemical, physical, biological, pharmacological, pharmaceutical, etc. properties of graphs corresponding to real life situations. The degree-based topological indices are used to correlate the physical and chemical properties of a molecule with its chemical structure. Boron nanotubular structures are high-interest materials due to the presence of multicenter bonds and have novel electronic properties. These materials have some important issues in nanodevice applications like mechanical and thermal stability. Therefore, they require theoretical studies on the other properties. In this paper, we compute the third Zagreb index, harmonic index, forgotten index, inverse sum index, modified Zagreb index and symmetric division deg index by applying subdivision and semi total point graph for boron triangular and boron-alpha nanotubes.

Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7

In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometric-arithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.