相关论文: On general Sombor index

The zeroth-order general Randi\'c index (usually denoted by $R_{\alpha}^{0}$) and variable sum exdeg index (denoted by $SEI_{a}$) of a graph $G$ are defined as $R_{\alpha}^{0}(G)= \sum_{v\in V(G)} (d_{v})^{\alpha}$ and $SEI_{a}(G)=…

The concept of the \emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\emph{directed graphs by definition}),…

Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called…

In this paper, we investigate the packing parameters in graphs. By applying the Mantel's theorem, We give upper bounds on packing and open packing numbers of triangle-free graphs along with characterizing the graphs for which the equalities…

In structural pattern recognition, given a set of graphs, the computation of a Generalized Median Graph is a well known problem. Some methods approach the problem by assuming a relation between the Generalized Median Graph and the Common…

We introduce a generalized thermostatistics based on Kolmogorov-Nagumo averages and appropriately selected information measures. The formalism includes Tsallis non-extensive thermostatistics, but also extensive thermostatistics based on…

We propose a framework for thinking about eccentricity in terms of blocks. We extend the familiar definitions of radius and center to blocks and verify that a central block contains all central points. We classify graphs into two types…

We derive normal approximation bounds for generalized $U$-statistics of the form \begin{equation*} S_{n,k}(f):=\sum_{ 1 \leq \beta (1),\dots,\beta (k) \leq n \atop \beta (i)\ne\beta (j), \ 1\leq i\ne j \leq k} f\big(X_{\beta…

In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…

We extend the Grundy number and the ochromatic number, parameters on graph colorings, to digraph colorings, we call them {\emph{digrundy number}} and {\emph{diochromatic number}}, respectively. First, we prove that for every digraph the…

In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…

The Wiener index of a connected graph is defined as the sum of the distances between all unordered pair of its vertices. In this paper, we characterize the graphs which extremize the Wiener index among all graphs on $n$ vertices with $k$…

In order to study the analytic properties of the Goldbach generating function we consider a smooth version, similar to the Chebyshev function for the Prime Number Theorem. In this paper, we obtain explicit numerical estimates for the…

Let $G=(V(G),E(G))$ be a simple graph with vertex set $V(G)=\{v_{1},v_{2},\cdots, v_{n}\}$ and edge set $E(G)$. The $p$-Sombor matrix $\mathcal{S}_{p}(G)$ of $G$ is the square matrix of order $n$ whose $(i,j)$-entry is equal to…

In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…

We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.

We investigate how small the Randi\'c index of a graph can be in terms of its matching number, and prove several results. We give best-possible linear bounds for graphs of small excess and for subcubic graphs; in the former case the size of…