Index Of Graph Research Articles

Unveiling novel eccentric neighborhood forgotten indices for graphs and gaph operations: A comprehensive exploration of boiling point prediction

<abstract><p>This paper marks a significant advancement in the field of chemoinformatics with the introduction of two novel topological indices: the forgotten eccentric neighborhood index (FENI) and the modified forgotten eccentric neighborhood index (MFENI). Uniquely developed for predicting the boiling points of various chemical substances, these indices offer groundbreaking tools in understanding and interpreting the thermal properties of compounds. The distinctiveness of our study lies in the in-depth exploration of the discriminative capabilities of FENI and MFENI. Unlike existing indices, they provide a nuanced capture of structural features essential for determining boiling points, a key factor in drug design and chemical analysis. Our comprehensive analyses demonstrate the superior predictive power of FENI and MFENI, highlighting their exceptional potential as innovative tools in the realms of chemoinformatics and pharmaceutical research. Furthermore, this study conducts an extensive investigation into their various properties. We present explicit results on the behavior of these indices in relation to diverse graph types and operations, including join, disjunction, composition and symmetric difference. These findings not only deepen our understanding of FENI and MFENI but also establish their practical versatility across a spectrum of chemical and pharmaceutical applications. Thus the introduction of FENI and MFENI represents a pivotal step forward in the predictive analysis of boiling points, setting a new standard in the field and opening avenues for future research advancements.</p></abstract>

Sombor index of uniform hypergraphs

<p>In 2021, Gutman proposed a topological index for graphs known as the Sombor index. In this paper, we obtain several upper and lower bounds of the Sombor index of uniform hypergraphs, including those of hypertrees. Furthermore, we present a Nordhaus-Gaddum type result for the Sombor index of uniform hypergraphs.</p>

On Vertex-Edge and Edge-Vertex Connectivity Indices of Graphs

On Vertex-Edge and Edge-Vertex Connectivity Indices of Graphs

Proof of a Conjecture on Symmetric Division Deg Index of Graphs

Proof of a Conjecture on Symmetric Division Deg Index of Graphs

Study of Topological Behavior of Some Computer Related Graphs

Network theory is the study of graphs such as representing equilibrium relationships or unequal relationships between different objects. A network can be defined as a graph where nodes and / or margins have attributes (e.g. words). Topological index of a graph is a number that helps to understand its topology and a topological index is known as irregularity index if it is greater than zero and topological index of graph is equal to zero if and only if graph is regular. The irregularity indices are used for computational analysis of nonregular graph topological composition. In this paper, we aim to compute topological invariants of some computer related graph networks. We computed various irregularities indices for the graphs of OTIS swapped network OPa and Biswapped Networks Bsw(Pa).

On Lanzhou Index of Graphs

Let G = ( V , E ) be a simple graph with vertex set V ( G ) and edge set E ( G ) . The Lanzhou index of a graph G is defined by L z ( G ) = ∑ u ∈ V ( G ) d 2 u ¯¯¯ d u , where d u ( ¯¯¯ d u resp.) denotes the degree of the vertex u in G ( ¯¯¯¯ G , the complement graph of G resp.). It has predictive powers to provide insights of chemical relevant properties of chemical graph structures. In this paper we discuss some properties of Lanzhou index. Several inequalities having lower and upper bound for the Lanzhou index in terms of first, second and third Zagreb indices, radius of graph, eccentric connectivity index, Schultz index, inverse sum indeg index and symmetric division deg index, are discussed. At the end the Lanzhou index of corona and join of graphs have been derived.

ON THE PRODUCT OF GEOMETRIC-ARITHMETIC, SOMBOR AND FIRST ZAGREB INDICES

Assume Ω is a connected and simple graph with edge set E(Ω) and vertex set V (Ω). In chemical graph theory, the Geometric-Arithmetic index, Sombor index, and first Zagreb index of graph are three well-defined and studied topological indices. In the present study, we introduce the new graph invariant, we call it as GSM(Ω) index, this new graph invariant is the product of Geometric-Arithmetic index, Sombor index, and first Zagreb index. Furthermore we discuss the effect on GSM(Ω) of inserting and deleting an edge into a graph Ω. In addition, we investigate the connections between the GSM(G) index and various well-studied topological indices.We discussed nano JD*-Homeomorphisms in nano topological spaces in this study. We address the fundamental characteristics and noteworthy characterizations of nano JD*-Homeomorphisms in nano topological spaces. Our analysis demonstrates how they relate to other ideas already known, such as nano semihomeomorphisms, nano pre-homeomorphisms, and nano g-homeomorphisms

Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Recently, graphs have started to be used to represent a finite ring. Nikmehr and Khojasteh in the article defined the nilpotent graph of a ring . Denoted , is a graph with the set of vertices being all the elements in the ring Two vertices and are adjacent if and only if is nilpotent elements in the ring . Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices. In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.

Tight bounds on the chromatic edge stability index of graphs

The chromatic edge stability index esχ′(G) of a graph G is the minimum number of edges whose removal results in a graph with smaller chromatic index. We give best-possible upper bounds on esχ′(G) in terms of the number of vertices of degree Δ(G) (if G is Class 2), and the numbers of vertices of degree Δ(G) and Δ(G)−1 (if G is Class 1). If G is bipartite we give an exact expression for esχ′(G) involving the maximum size of a matching in the subgraph induced by the vertices of degree Δ(G). Finally, we consider whether a minimum mitigating set, that is a set of size esχ′(G) whose removal reduces the chromatic index, has the property that every edge meets a vertex of degree at least Δ(G)−1; we prove that this is true for some minimum mitigating set of G, but not necessarily for every minimum mitigating set of G.

General Zagreb indices of composite graphs

General Zagreb indices of composite graphs

On physical analysis of entropy measures for sodium oxide via statistical models

AbstractThis study delves into a comprehensive physical analysis of entropy measures applied to sodium oxide . A key idea in information theory and thermodynamics, entropy is essential to comprehending the stability of a system. The study clarifies the intricate relationships and physical properties of by combining theoretical analysis with statistical methods, providing important knowledge for material design and industrial operations. In a chemical graph, atoms are shown by vertices while their bonding are illustrated by edges. Sodium oxide is a major contributor to manufacture glass, it also has potential applications in sequestration, transparent materials, biomedical devices and nano grating glass. A topological index is a relationship between the molecular graph and its topology. We have computed various graph entropies based on different topological indices of chemical graph of sodium oxide. Further we have integrated these graph entropies with distinct thermodynamical measures of sodium oxide by developing mathematical models between both quantities. We have developed these mathematical frameworks in MATLAB. All the models are selected relying on the least mean squared error or sum of squared error.

A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices

In the field of cheminformatics, the amalgamation of graph theory, chemistry, along with technology facilitates the establishment of connections between the structural as well as physiochemical attributes of organic compounds by employing certain valuable graph invariants including the corresponding molecular graph. In this work, we examine reverse topological indices, for instance, the reverse Zagreb index, the reverse arithmetic-geometric, the geometric-arithmetic, the reverse Nirmala indices for the bistar graphs B(n;m) , the reverse sum-connectivity index, the reverse Sombor as well as the corona product of Km∘K′n.

Explication of crossroads order based on Randic index of graph with fuzzy information

Explication of crossroads order based on Randic index of graph with fuzzy information

A novel nomogram integrated with preablation stimulated thyroglobulin and thyroglobulin/thyroid-stimulating hormone ratio to predict the therapeutic response of intermediate‑ and high‑risk differentiated thyroid cancer patients: a bi-center retrospective study.

To investigate the factors influencing the outcome of radioactive iodine (RAI) treatment in intermediate- to high-risk patients with differentiated thyroid carcinoma (DTC). We enrolled 553 DTC patients who underwent total thyroidectomy and categorized them into two groups according to their response to RAI therapy: excellent response (ER) and non-ER groups. Clinical and pathological characteristics of the patients were collected and retrospectively analyzed using univariate and multivariate binary logistic regression. Receiver operating characteristic (ROC) curves and diagnostic cutoff values were analyzed to assess the predictive value of important quantitative influences on 131I treatment outcomes. A new nomogram model was developed based on the above independent risk factors. R software was used to develop nomograms with all the independent prognostic factors included. The multivariate analysis showed that lymph node metastasis (LNM), stimulated thyroglobulin (sTg), thyroglobulin antibodies (TgAb), and sTg/thyroid-stimulating hormone (TSH) were significantly associated with non-ER of DTC patients. In the training set, the consistency index (C-index) of the new column line graph was 0.868 (95% CI 0.865-0.871). We proposed a new nomogram to predict non-ER for DTC with excellent discrimination and calibration.

Sharp upper bound on the Sombor index of bipartite graphs with a given diameter

Sharp upper bound on the Sombor index of bipartite graphs with a given diameter

A lower bound on the modified Randić index of line graphs

The modified Randić index of a graph G is denoted by R′(G)=∑uv∈E(G)1maxd(u),d(v), where d(u) is the degree of vertex u. Wang et al. (2023), Zhang and Wu (2022) obtained the lower bounds of Randić index and harmonic index of the line graph of any tree of T with n≥3, i.e. R(L(T))>n4 and H(L(T))>n4. In this paper, we consider the modified Randić index of the line graph of any tree T with n≥3, which implies the results of Wang et al. (2023), Zhang and Wu (2022).

Graphs with given connectivity and their minimum Sombor index having applications to QSPR studies of monocarboxylic acids

The Sombor index, introduced by Gutman in 2021, represents a novel graphical topological descriptor reliant upon graph degree information. It holds promise for elucidating the thermodynamic behavior of compounds. Denoting by Vnk (respectively, Enk) the set encompassing all connected graphs comprising n vertices with a specific vertex-connectivity (correspondingly, edge-connectivity) value of k. In Problem 1 (resp. Problem 2) of Hayat et al. (2022) [33], the question of finding minimum Sombor index of graphs in Vnk (resp. Enk) is proposed. In this note, we solve both of the open problems by characterizing minimizing graphs in Enk and Vnk corresponding to the Sombor index. We employed commonly occurring valency-based graphical indices in a QSPR studies of the physicochemical characteristics for monocarboxylic acids. The proposed statistical models infer that the Sombor index predicts various physicochemical characteristics for monocarboxylic acids having strong predictive coefficients such as ρ=0.99998.

Structure-property modeling for thermodynamic properties of benzenoid hydrocarbons by temperature-based topological indices

Quantitative structure-property relationship (QSPR) modeling employs contemporary mathematical tools to predict physicochemical, thermodynamic and biological properties of compounds from their chemical structures. Graphical indices provide those mathematical tools and efficiently correlate physicochemical, thermodynamic and biological properties of compounds. This paper considers the class of benzenoid hydrocarbons (BHs) and investigates the predictive power of commonly occurring graphical temperature indices for determining thermodynamic characteristics of BHs. The entropy (So) & heat capacity (Cp) have been selected to advocate for thermodynamic characteristics. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data is also publicly available. First, a computer-based method is put forwarded to evaluate temperature indices of a chemical graph. The computational method is, then, employed to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of Cp and So for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, quadratic. Unexpectedly, some underresearched temperature indices like the general first & second temperature indices perform well having the correlation coefficient >0.9 which is the minimum threshold in a comparative testing. Based on our statistical analysis, three recently proposed temperature indices perform exceptionally well in comparison with all the existing temperature indices. The results suggest their further employability in QSPR modeling. Importantly, our research contributes towards countering proliferation of graphical indices.

Bounds of Fibonacci-sum graph for some distancebased topological indices and an application on BFS algorithm

The aim of this study is to obtain the lower and upper bounds for the distance-based Wiener index, Hyper-Wiener index and Harary index of the Fibonacci-sum graph. Firstly, the shortest distance of the vertices in the Fibonacci-sum graph is characterized. Afterwards, the numbers of decision vertices and leaves are obtained by applying the BFS algorithm to the Fibonacci-sum graph.

Inverse Problem for Leap Zagreb Indices

Inverse Problem for Leap Zagreb Indices