Index Of Graph Research Articles

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.

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.

Smallest ABS index of unicyclic graphs with given girth

Smallest ABS index of unicyclic graphs with given girth

ZAGREB INDICES OF A NEW SUM OF GRAPHS

The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed the first and second Zagreb indices of four new operations on a graph defined by M. Eliasi, B. Taeri in [4]. Motivated from this we define a new operation on graphs and compute the first and second Zagreb indices of the resultant graph. We illustrate the results with some examples.

Indices from visibility graph complexity of spontaneous speech signal: An efficient nonlinear tool for Alzheimer's disease diagnosis

Interest in dynamical data analytics of human speech related to the diagnosis of Alzheimer's disease (AD) has recently risen. This study aims to scrutinize the dynamic variations in AD speech based on concepts called complexity and fractality. Towards this goal, the visibility graph (VG) of the spontaneous speech time series as a quantitative approach is proposed to distinguish healthy subjects from those with Alzheimer's. The dynamical patterns of the speech signals are analyzed between three stages of AD and healthy subjects by examining some specific kinds of these measures, known as graph index complexity (GIC) and power of scale-freeness (PS) in VG. The results show the practical ability of the GIC and PS to detect the underlying pathological mechanism of Alzheimer's disease. In addition, it is found that all speech series have visibility graphs with a power-law topology, and fractality in them is reflected by a mechanism related to the brain system pathology, which affects the language skills of people.

Forgotten Index and Forgotten Coindex of Graphs

Forgotten Index and Forgotten Coindex of Graphs

Chemical Applicability of Second Order Sombor Index

In this paper, we introduce the higher-order Sombor index of a molecular graph. In addtition, we compute the second order Sombor index of some standard class of graphs and line graph of subdivision graph of 2D-lattice, nanotube and nanotorus of TUC_4C_8[p,q] and also we obtain the expressions of the second order Sombor index of the line graph of subdivision graph of tadpole graph, wheel graph, ladder graph and chain silicate network CSn. Further, we study the linear regression analysis of the second order Sombor index with the entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers.

Topological Indices of the Relative Coprime Graph of the Dihedral Group

Topological Indices of the Relative Coprime Graph of the Dihedral Group

Some indices of picture fuzzy graphs and their applications

Some indices of picture fuzzy graphs and their applications