On some degree based topological indices of mk-graph

2012

A topological representation of a molecule can be carried out through molecular graph. The descriptors are numerical values associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. A topological index is the graph invariant number calculated from a graph representing a molecule. The most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph G or to topological distances in G. In this paper we introduce an edge operation ˆ e on the graphs 1 G and 2 G such that resulting graph 12 ˆ Ge G has an edge introduced between arbitrary vertex of 1

Symmetry

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

Journal of Interdisciplinary Mathematics, 2022

To study the properties such as physical and chemical of compounds, the topological indices are introduced in chemical graph theory. These indices provide qualitative structure activity relationship (QSAR). Degree based topological indices are commonly used invariant in chemical graph theory. However, in this article, a new degree of vertices is introduced, called "deficiency degree". Further, we have computed five topological indices based on the deficiency degree like "deficient first Zagreb index, deficient generalized Randić index, deficient harmonic index, deficient inverse sum index, deficient augmented Zagreb index" for identified graphs using the M-polynomial of graph.

Journal of Chemistry, 2021

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

Mathematical Problems in Engineering

In mathematical chemistry, molecular structure of any chemical substance can be expressed by a numeric number or polynomial or sequence of number which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structure are studied and obtained their exact results for sum degree-based indices. Additionally, a comparison is shown graphically among all the indices.

Journal of Mathematics

Topological indices are numeric values associated with a graph and characterize its structure. There are various topological indices in graph theory such as degree-based, distance-based, and counting-related topological indices. Among these indices, degree-based indices are very interesting and studied well in literature. In this work, we studied the generalized form of harmonic, geometric-arithmetic, Kulli–Basava indices, and generalized power-sum-connectivity index for special graph that are bridge graph over path, bridge graph over cycle, bridge graph over complete graph, wheel graph, gear graph, helm graph, and square lattice graph. We found exact values for the stated indices and for the stated special graphs. We also investigated the generalized form of the indices for various properties of alkane isomers, from which we obtained interesting results which are closed to that of experimental obtained results.

2021

Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It's found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced second Zagreb index RM 2 , and the reduced reciprocal Randić index (RRR). If d 1 , d 2 , . . . , d n are the degrees of the vertices of the graph G = (V, E), then

ArXiv, 2018

There are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, and so forth are used to characterize the chemical compound. In this paper we computed the edge version of atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, geometric-arithmetic index and fifth geometric-arithmetic index of Double-wheel graph and Hanoi graph. The results are analyzed and the general formulas are derived for the above mentioned families of graphs.