相关论文: Topological indices in Random Spiro Chains
In this paper, we examine a specific type of random chains and propose an unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values…
In chemical graph theory, caterpillar trees have been an appealing model to represent the molecular structures of benzenoid hydrocarbon. Meanwhile, topological index has been thought of as a powerful tool for modeling quantitative…
In this article, we investigate the Zagreb index, a kind of graph-based topological index, of several random networks, including a class of networks extended from random recursive trees, plain-oriented recursive trees, and random…
The Sombor indices, a new category of degree-based topological molecular descriptors, have been widely investigated due to their excellent chemical applicability. This paper aims to establish Sombor indices distributions in random polygonal…
In this paper, we characterize the structure and topological indices of a class of random spider trees (RSTs) such as degree-based Gini index, degree-based Hoover index, generalized Zagreb index and other indices associated with these. We…
A topological index is a real number which is derived from a network or a graph by mathematically that characterizes the whole of its structural properties. Recently, there are various topological indices that have been introduced in…
In this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this…
In this paper we give new bounds for a several vertex-based and edge-based topological indices of graphs: Albertson irregularity index, degree variance index, Mostar and the first Zagreb index. Moreover, we give a new upper bound for the…
Ordered pivotal sampling is one of the simplest algorithm to perform without-replacement unequal probability sampling. It has found uses in the context of longitudinal surveys and spatial sampling, and enables in particular a good spatial…
The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the first variable Zagreb index $M_1^\alpha$, and to characterize the set of extremal graphs with respect to them. Our main…
In the investigation of limits of Markov chains, the presence of states which become instantaneous states in the limit may prevent the convergence of the chain in the Skorohod topology. We present in this article a weaker topology adapted…
We perform a detailed computational study of the recently introduced Sombor indices on random graphs. Specifically, we apply Sombor indices on three models of random graphs: Erd\"os-R\'enyi graphs, random geometric graphs, and bipartite…
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…
Topological indices play a significant role in mathematical chemistry. Given a graph $\mathcal{G}$ with vertex set $\mathcal{V}=\{1,2,\dots,n\}$ and edge set $\mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological…
In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, we have inequalities for these indices relating them with other indices: the first Zagreb index, the forgotten index and the first variable…
The Zagreb index, which is defined as the sum of squares of degrees of the nodes of a tree, was studied in previous works by martingale techniques for random non-plane recursive trees and classes of random trees which are close to random…
Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. We show that the number of…
The aim of this paper is to obtain new inequalities for a large family of topological indices restricted to unicyclic graphs and to characterize the set of extremal unicyclic graphs with respect to them. This family includes variable first…
We consider topological indices I that are sums of f(deg(u)) f(deg(v)), where {u,v} are adjacent vertices and f is a function. The Randi{\'c} connectivity index or the Zagreb group index are examples for indices of this kind. In earlier…
Motivated by the recently introduced topological index, the Somber index, we define a new topological index of a graph in this paper, we call it Sombor coindex. The Sombor coindex is defined by considering analogous contributions from the…