Index Of Graph Research Articles

Harary index, binding number and toughness of graphs

Given a connected (molecular) graph G, its Harary index H(G) is defined by the reciprocal sum of the distances between all unordered pairs of vertices of G. Lower bounds on the graph vulnerability parameters binding number and toughness have been often used to determine that the graph has a certain property. Recently, Yatauro [Discrete Appl. Math. 338 (2023) 56-68] gave a sharp upper bound of W(G) (Wiener index) to ensure that G has a determined lower bound (greater than or equal to 1) for the binding number or toughness. In this paper, we supply an upper bound on H(G) to ensure that G has a determined lower bound (between 0 and 1) for the binding number or toughness, and show that these bounds are best possible in some sense.

On weighted forgotten index of total transformation graphs

In QSPR studies topological indices plays vital role. To enrich this field we put forward novel topological indices namely weighted Zagreb indices. In this paper we give explicit formulae for weighted Zagreb indices of total transformation graphs in terms of elements of a graph G.

Some polynomials and degree-based topological indices of molecular graph and line graph of Titanium dioxide nanotubes

Graph polynomials based on distance and degree are helpful and necessary because they contain much information about topological indices. In this article, the general inverse sum indeg index and the generalized inverse sum indeg polynomials are calculated for the molecular graph and the line graph of the Titanium dioxide nanotubes. Then, with their help, some polynomials and some degree-based topological indices of the molecular graph and the line graph of Titanium dioxide nanotubes are obtained.

On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

<p>Let $ G = (V(G), E(G)) $ be a simple connected graph with vertex set $ V(G) $ and edge set $ E(G) $. The atom-bond sum-connectivity (ABS) index was proposed recently and is defined as $ ABS(G) = \sum_{uv\in E(G)}\sqrt{\frac{d_{G}(u)+d_{G}(v)-2}{d_{G}(u)+d_{G}(v)}} $, where $ d_{G}(u) $ represents the degree of vertex $ u\in V(G) $. A connected graph $ G $ is called a unicyclic graph if $ |V(G)| = |E(G)| $. In this paper, we determine the maximum ABS index of unicyclic graphs with given diameter. In addition, the corresponding extremal graphs are characterized.</p>

The minimal degree Kirchhoff index of bicyclic graphs

<abstract><p>The degree Kirchhoff index of graph $ G $ is defined as $ Kf^{*}(G) = \sum\limits_{{u, v}\subseteq V(G)}d(u)d(v)r_{G}(u, v) $, where $ d(u) $ is the degree of vertex $ u $ and $ r_{G}(u, v) $ is the resistance distance between the vertices $ u $ and $ v $. In this paper, we characterize bicyclic graphs with exactly two cycles having the minimum degree Kirchhoff index of order $ n\geq5 $. Moreover, we obtain the minimum degree Kirchhoff index on bicyclic graphs of order $ n\geq4 $ with exactly three cycles, and all bicyclic graphs of order $ n\geq4 $ where the minimum degree Kirchhoff index has been obtained.</p></abstract>

On the Eigenvalues and Energy of the Seidel and Seidel Laplacian Matrices of Graphs

Let S(Γ) be a Seidel matrix of a graph Γ of order n and let D(Γ) = diag(n − 1 − 2d1, n − 1 − 2d2, …, n − 1 − 2dn) be a diagonal matrix with di denoting the degree of a vertex vi in Γ. The Seidel Laplacian matrix of Γ is defined as SL(Γ) = D(Γ) − S(Γ). In this paper, we obtain an upper bound, and a lower bound on the Seidel Laplacian Estrada index of graphs. Moreover, we find a relation between Seidel energy and Seidel Laplacian energy of graphs. We establish some lower bounds on the Seidel Laplacian energy in terms of different graph parameters. Finally, we present a relation between Seidel Laplacian Estrada index and Seidel Laplacian energy of graphs.

Newly defined fuzzy Misbalance Prodeg Index with application in multi-criteria decision-making

<abstract><p>In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of $ 1 $ or $ 0 $, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multi-criteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices.</p></abstract>

The second Hyper-Zagreb index of VC5C7[p, q] and HC5C7[p, q] nanotubes

The first and second Hyper-Zagreb indices are the molecular descriptors that describe the structures of chemical compounds and they help us to predict certain physicochemical properties. In this paper, we studied the first and second Hyper-Zagreb indices for certain important chemical structures like line graphs of the VC5C7 [p, q] and 5 7HC C [p, q] nanotubes. Moreover, we defined second Hyper-Zagreb-polynomial of graph G and applied it on the line graphs of the 5 7VC C [p, q] and 5 7HC C [p, q] nanotubes. These explicit formulae can correlate the chemical structure of molecular graph of nanotube to information about their physical structure.

Extremal reformulated forgotten index of trees, unicyclic and bicyclic graphs

Extremal reformulated forgotten index of trees, unicyclic and bicyclic graphs

Valor diagnóstico de análises lineares e não lineares da variabilidade da frequência cardíaca para diferenciação da homeostase em estado de saúde, doença e risco de óbito em cães

ABSTRACT The autonomic nervous system is closely linked to heart rate and is characterized as a chaotic deterministic system. As the heart is therefore controlled by a non-linear system, these analyzes are being used more and more. The aim of this study was to evaluate nonlinear indices of recurrence graphs and linear indices in healthy, sick and at risk of death dogs and to demonstrate whether these indices have good diagnostic accuracy to identify dogs at risk of death. Sixty-six dogs underwent heart rate variability analysis using a frequency meter. The results showed that the SDNN, RMSSD, PNN50% and DET% indices showed a significant difference between all groups, helping to differentiate the health status in terms of autonomic homeostasis. Greater sensitivity (96.67%) was observed for linear indices (SDNN, RMSSD and PNN50%) and greater specificity (100%) for non-linear indices (DET%, REC% and LAM%) in the recognition of dogs at risk of death. Linear indices (SDNN, RMSSD and PNN50%) and non-linear indices (DET% and ShanEnt) showed greater diagnostic accuracy for identifying healthy or dying dogs. It is concluded that the studied indices of heart rate variability help to differentiate the health status in healthy dogs and are excellent predictors of prognosis.

SOME ZAGREB-TYPE INDICES OF VICSEK POLYGON GRAPHS

Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs.

Prediction of the Boiling Point of Acrylate and Methacrylate Polymers Through Wiener Index

Wiener index, a topological index of a molecular graph of the molecules are widely used to study the physico-chemical properties of the molecules. We considered the molecules, acrylate and methacrylate polymers. The Wiener index of these two polymers are obtained. And using this, the boiling point of these two polymers are studied extensively. Also, the detailed comparison is described graphically.

The Maximum and Minimum Value of Exponential Randić Indices of Quasi-Tree Graph

The Maximum and Minimum Value of Exponential Randić Indices of Quasi-Tree Graph

Extremal Graphs with Respect to Vertex–Degree–Based Topological Indices for c-Cyclic Graphs

Extremal Graphs with Respect to Vertex–Degree–Based Topological Indices for c-Cyclic Graphs

Maximum and Minimum Lanzhou Index of c-Cyclic Graphs

Maximum and Minimum Lanzhou Index of c-Cyclic Graphs

REDUCED ELLIPTIC AND MODIFIED REDUCED ELLIPTIC INDICES OF SOME CHEMICAL STRUCTURES

In this paper, we introduce the reduced elliptic index, the modified reduced elliptic index and their corresponding exponentials of a graph. Also we determine these newly defined elliptic indices for some standard graphs, jagged-rectangle benzenoid systems and polycyclic aromatic hydrocarbons which are appeared in Mathematical Chemistry

Szeged Indices of Bicyclic Graphs with Applications as Molecular Descriptor

Szeged Indices of Bicyclic Graphs with Applications as Molecular Descriptor

Extremal graphs and bounds for general Gutman index

<p>For a connected graph $ G, $ the general Gutman index was denoted by $ Gut_{a, b}(G) $ and was given by $ Gut_{a, b}(G) = \sum\limits_{\left\{u, v\right\}\subseteq V(G)} \left[d_{G}(u)d_{G}(v)\right]^a \left[d_{G}\left(u, v\right)\right]^b $, where $ a, b \in \mathbb{R} $, $ d_G(x) $ was the degree of vertex $ x $ in $ G $ and $ d_G(u, v) $ denoted the distance between vertices $ u $ and $ v $ in $ G $. In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.</p>

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>

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

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