Some New Upper Bounds for the Y -Index of Graphs (original) (raw)
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Bounds for the Topological Indices of ℘ graph
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.
Journal of inequalities and applications, 2017
Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-chemical properties and topological indices such as Zagreb, Randić and multiple Zagreb indices. In this paper, we determine the lower and upper bounds of Zagreb indices, the atom-bond connectivity (ABC) index, multiple Zagreb indices, the geometric-arithmetic (GA) index, the forgotten topological index and the Narumi-Katayama index for the Cartesian product of F-sum of connected graphs by using combinatorial inequalities.
On the general zeroth-order Randić index of bargraphs
2019
In graph theory, an invariant of a graph is a numerical quantity that depends only on its abstract structure, not on graph representations such as particular labeling or drawing of the graph. A topological index is an invariant of a molecular graph associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Nowadays, there exists a legion of topological indices with some applications in chemistry, especially in QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship) studies [18]. Since topological indices have gained considerable popularity recently, many new topological indices have been proposed and studied in the mathematical chemistry literature. In 1975, Randić introduced the connectivity index [17], which is one of the the most studied and applied topological indices in QSPR and QSAR researches, defined by
Polynomial and Deficient Topological Indices of Identified Graphs
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.
On the Reformulated Second Zagreb Index of Graph Operations
Journal of Chemistry, 2021
Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the graphs in QSAR/QSPR investigation. The reformulated second Zagreb index (RSZI) is such a novel TI having good correlations with various physical attributes, chemical reactivities, or biological activities/properties. The RSZI is defined as the sum of products of edge degrees of the adjacent edges, where the edge degree of an edge is taken to be the sum of vertex degrees of two end vertices of that edge with minus 2. In this study, the behaviour of RSZI under graph operations containing Cartesian product, join, composition, and corona product of two graphs has been established. We have also applied these results to compute RSZI for some important classes of molecular graphs and nanostructures.
On some degree based topological indices of mk-graph
Journal of Discrete Mathematical Sciences and Cryptography, 2020
A topological index is a real number which is same under graph isomorphism and it is derived from a graph by mathematically. In chemical graph theory, a molecular graph is a simple graph having no loops and multiple edges in which atoms and chemical bonds are represented by vertices and edges respectively. Topological indices defined on these chemical molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. In this paper, we compute general expressions
On Generalized Topological Indices for Some Special Graphs
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.
Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs
Discrete Dynamics in Nature and Society, 2021
A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total - electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randic are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized - sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized - sum graphs as the consequences of the obtained results. At the end, - graphical presentations are also included to illustrate the results for better understanding.
On General Reduced Second Zagreb Index of Graphs
Mathematics
Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous substances, etc. The graph invariant GRMα, known under the name general reduced second Zagreb index, is defined as GRMα(Γ)=∑uv∈E(Γ)(dΓ(u)+α)(dΓ(v)+α), where dΓ(v) is the degree of the vertex v of the graph Γ and α is any real number. In this paper, among all trees of order n, and all unicyclic graphs of order n with girth g, we characterize the extremal graphs with respect to GRMα(α≥−12). Using the extremal unicyclic graphs, we obtain a lower bound on GRMα(Γ) of graphs in terms of order n with k cut edges, and completely determine the corresponding extremal graphs. Moreover, we obtain several upper bounds on GRMα of different classes of graphs in terms of order n, size m, independence number γ, chromatic number k, etc. In particular, we present an u...