Index Of Graph Research Articles

A Novel Approach to Investigate Sadhana and PI Indices

A topological index is a number used in QSAR and QSPR research to assess the structural properties of a graph. The Sadhana and PI, polynomial-based topological indices, have been intensively explored in the study of chemical graph theory since a few years ago. These indices are computed using their related polynomials, however, in this study, we use an instantaneous and revolutionary approach to compute these indices for hexagonal boron nitride graphs and carbon nanotube structures.

Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy So and the heat capacity Cp have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both Cp and So is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity (ABC2) index, the total eccentricity (ζ) index, and the eccentric-connectivity (ξ) index outperform the well-researched descriptors such as the Szeged (Sz), the Wiener W, the Padmakar-Ivan (PI) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the ABC2 index showcases the mean correlation coefficient ρ>0.95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy So and the heat capacity Cp of linear polyacenes.

Steiner Distance Related Parameters of Wheel graphs

For a connected graph of order at least and the Steiner distance among the vertices of is the minimum size among all the connected subgraphs whose vertex sets contain In this paper, we calculate the Steiner distance parameters such as Steiner degree distance, Steiner Gutman index, Steiner Harary index and Steiner reciprocal degree distance of a wheel graphs.

The visibility graph analysis of heart rate variability during chi meditation and Kundalini Yoga techniques

The human heartbeat reflects one of the most crucial types of complex physiologic fluctuations. The purpose of this study is to study and evaluate the complexity of heart rate time series to capture its intrinsic multiscale dynamics based on the concept of fractality and complexity. The visibility graph (VG) of the heart rate series is proposed as a quantitative method to differentiate subjects in rest and meditation periods of two techniques: Chi meditation and Kundalini Yoga meditation. Differential complexities between the two mentioned states are quantified using the power of scale-freeness (PS) and the graph index complexity (GIC) in VG. The model is applied to available heart rate signals in the PhysioBank. The results reveal the promising ability of PS and GIC to assess the distinction between the two states. However, in both meditation techniques, the complexities of heart rate signals are increased during meditation. The results also show all heart rate series have visibility graphs with a power-law topology, and fractality in the heart rate series is dictated by a mechanism associated with the chaotic nature of the biological signals that could be useful to evaluate heart rate signals during meditation.

On the Lanzhou index of graphs

Let $G$ be a simple graph with vertex set $V(G)$ and edge set $E(G)$. The Lanzhou index of a graph $G$ is defined as ${\rm Lz}(G)=\sum_{u\in V(G)}\,d_{\overline{G}}(v)\,d_G(v)^2$, where $d_G(v)$ denotes the degree of the vertex $v$ in $G$. In this paper, we determine extremal values of the Lanzhou index in terms of some graph parameters, as well as Nordhaus--Gaddum--type results. We also find relations between Lanzhou Index and other topological indices.

Several Zagreb indices of power graphs of finite non-abelian groups

Molecular topology can be described by using topological indices. These are quantitative measures of the essential structural features of a proposed molecule calculated from its molecular structure. It is a numerical value obtained from a molecular configuration that reflects the significant physical characteristics of the suggested molecule. Numerous physical properties, chemical reactivity, and biological activity are correlated with the chemical composition using an algebraic number. The power graph P(G) of a finite group G is a graph whose vertex set is G and in which two distinct vertices are connected by an edge when one element is an integral power of the other. This article investigates a wide range of degree-based topological descriptors for power graphs of various finite groups. We find numerous Zagreb indices (given in Table 1) of power graphs of finite non-cyclic and cyclic groups, dihedral, and generalized quaternion groups.

On (exponential) bond incident degree indices of graphs

On (exponential) bond incident degree indices of graphs

COMPUTATION OF b-CHROMATIC TOPOLOGICAL INDICES OF SOME GRAPHS AND ITS DERIVED GRAPHS

The two fastest-growing subfields of graph theory are graph coloringand topological indices. Graph coloring is assigning the colors/values to theedges/vertices or both. A proper coloring of the graph G is assigning colors/valuesto the vertices/edges or both so that no two adjacent vertices/edges share the samecolor/value. Recently, studies involving Chromatic Topological indices that dealtwith different graph coloring were studied. In such studies, the vertex degrees getreplaced with the colors, and the computation is carried out based on the topologicalindex of our choice. We focus on b-Chromatic Zagreb indices and b-Chromaticirregularity indices in this work. This paper discusses the b-Chromatic Zagreb indicesand b-Chromatic irregularity indices of the gear graph, star graph, and itsderived graphs such as the line and middle graph.

Sharp bounds on the symmetric division deg index of graphs and line graphs

Sharp bounds on the symmetric division deg index of graphs and line graphs

Analysis of Hanoi graph by using topological indices

One of the main challenges in molecular science is to model a chemical complex and predict its thermochemical properties. Various researchers have developed a number of hypothetical techniques in this regard, and one of them is focused on the topological indices. A topological index is a number associated with a molecule’s structural graph that is considered to be capable of predicting certain chemical and physical properties of molecules. Degree-based topological indices are one of the groups of topological indices that are crucial in chemical graph theory. Shannon’s entropy is a fundamental factor of a subclass of topological indices that measures the structural information of the graphs. In this study, we examine the entropy based on topological indices such as the first and second Zagreb indices, the general Randić index, the harmonic and sum-connectivity index of Hanoi graph. Moreover, we determine a number of multiplicative invariants, and different polynomials for Hanoi graphs with graphical illustrations.

On the first Zagreb index of graphs with Self-Loops

Some of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index M 1 ( G ) of a graph G is defined as the sum of squares of the degrees of the vertices. Let X ⊆ V ( G ) and let G X be the graph obtained from the simple graph G, by attaching a self-loop to each of its vertices belonging to X. In this article, some sharp bounds for the first Zagreb index of graphs with self-loops using various parameters has been put forward.

Fuzzy Computational Analysis of Flower Graph via Fuzzy Topological Indices

Fuzzy graphs have many applications not only in mathematics but also in any field of science where the concept of fuzziness is involved. The notion of fuzziness is suitable in any environment, which favor to predicts the problem and solve this problem in a decent way. As compared to crisp theory, fuzzy graphs are a more beneficial and powerful tool to get better accuracy and precision due to their fuzziness property. A topological index is a numerical value which characterizes the properties of the graph. Topological indices were basically developed for chemical structures, but these are also used for general graphs as well. In chemical graph theory, topological indices are used to extract the chemical properties of the graphs. These indices are also well studied in fuzzy environment. Applications of fuzzy graphs are found in medicines, telecommunications, traffic light control, and many more. Our aim is to find these fuzzy topological indices for flower graphs to strengthen the concepts of fuzziness in general graphs. In this paper, some novel results for f m × r flower graphs are achieved.

Proofs to Some Open Problems on the Maximum Sombor Index of Graphs

Proofs to Some Open Problems on the Maximum Sombor Index of Graphs

A Study on the Energy of Graphs and Its Applications

In this paper, we dealt with two very well-known eigenvalue-based molecular descriptors such as the energy of graph ( E ( G ) ) and Estrada index ( E E ( G ) ) . We test their predictive potential of some physicochemical properties of polycyclic aromatic hydrocarbons using a data set of benzenoid hydrocarbons. We stabilized a relation of these two indices with some well-known degree-based topological indices such as the first Zagreb index, second Zagreb index, F-index, Randić index, Reciprocal Randić index, Atom bond connectivity index, sum-connectivity index, Geometric-arithmetic, Harmonic index, symmetric division deg index, and redefined Zagreb index.

Multi-Attribute Group Decision Making Based on Spherical Fuzzy Zagreb Energy

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as it enhances the space of uncertainty. It broadens the space of vague information evaluated by decision makers since graphs are the pictorial representation of information. Graphs are a tool to represent a network. To handle some real-world problems, spherical fuzzy graphs can be used more effectively as compared to picture fuzzy graphs (PFGs). In this article, we expand the notion of fuzzy Zagreb indices of the fuzzy graph to the spherical fuzzy Zagreb indices of the spherical fuzzy graph (SFG). The spherical fuzzy Zagreb matrix of SFG and Zagreb energy of SFG are defined with examples. Additionally, we develop several lower and upper bounds of the spherical Zagreb energy of SFG. In addition, we present an application of SFG by computing its Zagreb energy in the decision-making problem of choosing the best location for business purposes.

On the Rényi index of random graphs

On the Rényi index of random graphs

Rainbow connectivity and rainbow index of inhomogeneous random graphs

We investigate the rainbow k-connectivity rck and (t,k)-rainbow index rxt,k of the inhomogeneous random graph G(n,p), where any two vertices i and j are joined by an edge eij with probability p(eij) independently of all other edges, and p={p(eij)}. We show that the known threshold functions for the monotone properties rck(G(n,p))≤r and rxt,k(G(n,p))≤t for integers k,r and t in the Erdős–Rényi random graph G(n,p) can be extended to ‘threshold landscapes’ in terms of G(n,p). In contrast to the traditional plain thresholds characterized as a watershed, our threshold landscapes have two surfaces that are inherently interwoven with each other. This sheds some light on the network connectivity as appropriate trade-offs are allowed and is potentially applicable in network science where connections are not always equal.

The distinguishing index of graphs with infinite minimum degree

AbstractThe distinguishing index of a graph is the least number of colors necessary to obtain an edge coloring of that is preserved only by the trivial automorphism. We show that if is a connected ‐regular graph for some infinite cardinal then , proving a conjecture of Lehner, Pilśniak, and Stawiski. We also show that if is a graph with infinite minimum degree and at most vertices of degree for every infinite cardinal , then . In particular, if has infinite minimum degree and order at most .

Extreme and statistical properties of eigenvalue indices of simple connected graphs

We analyze graphs attaining the extreme values of various spectral indices in the class of all simple connected graphs, as well as in the class of graphs which are not complete multipartite graphs. We also present results on density of spectral gap indices and its nonpersistency with respect to small perturbations of the underlying graph. We show that a small change in the set set of edges may result in a significant change of the spectral index like, e.g., the spectral gap or spectral index. We also present a statistical and numerical analysis of spectral indices of graphs of the order m≤10. We analyze the extreme values for spectral indices for graphs and their small perturbations. Finally, we present the statistical and extreme properties of graphs on m≤10 vertices.

Schultz and Modified Schultz Polynomials of Edges Induce Chain and Ring for Hexagonal Graphs

Schultz polynomial is one of the must significant formulas that represent a relationship between the degree’s of vertices in a simple connected graph G and the distances between these vertices. In this work, Schultz and modified Schultz polynomials, as well as their topological indices of chain and ring hexagonal graphs, have been successfully identified.