相关论文: Note on PI and Szeged indices
For a (molecular) graph, the first multiplicative Zagreb index $\prod_1(G) $ is the product of the square of every vertex degree, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of the products of degrees of pairs of…
The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we…
In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry,…
The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations…
The \emph{eccentricity} of a vertex $u$ in a graph $G$, denoted by $e_G(u)$, is the maximum distance from $u$ to other vertices in $G$. We study extremal problems for the average eccentricity and the first and second Zagreb eccentricity…
A numerical parameter, referred to as a topological index, is used to represent the molecular structure of a compound by analyzing its graph-theoretical characteristics. Topological indices are predictive methods for the physicochemical…
Let $G$ be a connected graph with $n$ vertices and $m$ edges. The vertex-degree-based topological index (VDB) (or graphical function-index) $TI(G)$ of $G$ with edge-weight function $I(x,y)$ is defined as $$TI(G)=\sum\limits_{uv\in…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
The Kirchhoff index is defined as the sum of resistance distances between all pairs of vertices in a graph. This index is a critical parameter for measuring graph structures. In this paper, we characterize polygonal chains with the minimum…
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such…
In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalized Wiener polarity index $W_k (G)$ as the…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Let $G=(V,E)$ be a simple graph with $n = |V|$ vertices and $m = |E|$ edges. The first and second Zagreb indices are among the oldest and the most famous topological indices, defined as $M_1 = \sum_{i \in V} d_i^2$ and $M_2 = \sum_{(i, j)…
Many types of topological indices such as degree-based topological indices, distance-based topological indices and counting related topological indices are explored during past recent years. Among degree based topological indices, Zagreb…
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
The generalized hierarchical product of graphs was introduced by L. Barri\'ere et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…