相关论文: Mean Sombor index

The Sombor index $SO(G)$ of a graph $G$ is the sum of the edge weights $\sqrt{d^2_G(u)+d^2_G(v)}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of the vertex $u$ in $G$. A connected graph $G = (V ,E)$ is called a quasi-tree,…

Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor index and reduced Sombor index, were introduced by Gutman,…

Using inequalities is a good way of studying topological indices. Chemical graph theory is one of the nontrivial applications of graph theory. In this paper, we examine and calculate another degree-based topological index for…

Recently, the Euler Sombor index $(EUS)$ was introduced as a novel degree-based topological index. For a graph $G$, the Euler Sombor index is defined as $$EUS(G) = \sum_{v_i v_j \in E(G)} \sqrt{d_i^2 + d_j^2 + d_i d_j},$$ where $d_i$ and…

The Sombor index of a graph $G$, introduced by Ivan Gutman, is defined as the sum of the weights $\sqrt{d_G(u)^2+d_G(v)^2}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of vertex $u$ in $G$. The Sombor coindex is recently…

In this paper, the investigates Adriatic indices, specifically the sum lordeg index where it defined as $SL(G) = \sum_{u \in V(G)} \deg_G(u) \sqrt{\ln \deg_G(u)}$ and the variable sum exdeg index $SEI_a(G)$ for $a>0$, $a\neq 1$. We present…

Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let G^k_n be the set of all n-vertex connected…

Elliptic Sombor and Euler Sombor indices are recently defined topological indices using Sombor index. Elliptic sombor index is defined as $ESO(G)=\sum_{uv\in E(G)}(d_u+ d_v)\sqrt{d^2_u+ d^2_v}$ and Euler Sombor index is defined as $EU(G)=…

Sombor index is a novel topological index, which was introduced by Gutman and defined for a graph $G$ as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, where $d_{u}=d_{G}(u)$ denotes the degree of vertex $u$ in graph $G$.…

For a graph $G$ with edge set $E$, let $d(u)$ denote the degree of a vertex $u$ in $G$. The diminished Sombor (DSO) index of $G$ is defined as $DSO(G)=\sum_{uv\in E}\sqrt{(d(u))^2+(d(v))^2}(d(u)+d(v))^{-1}$. The cyclomatic number of a graph…

The Sombor index, a degree-based topological descriptor introduced by Gutman in 2021, lacks closed-form expressions for complex hierarchical trees with multi-level pendant structures and nonuniform degree distributions, despite extensive…

The numerical values extracted from a graph that indicates its topology are called topological indices. A contemporary and efficient method is to compute a graph's topological indices using the graph polynomial that corresponds to it. This…

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…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The Sombor and reduced Sombor indices of $G$ are defined as $SO(G)=\sum_{uv\in E(G)}\sqrt{deg_G(u)^2+deg_G(v)^2}$ and $SO_{red}(G)=\sum_{uv\in…

In this paper, degree-based topological indices play a key role in the structural analysis of graphs in this paper and have significant uses in chemical graph theory. We investigate the connections between three such tree indices: the…

Recently, based on elementary geometry, Gutman proposed several geometry-based invariants (i.e., $SO$, $SO_{1}$, $SO_{2}$, $SO_{3}$, $SO_{4}$, $SO_{5}$, $SO_{6}$). The Sombor index was defined as $SO(G)=\sum\limits_{uv\in…

Let $G$ be a graph and let $m_{ij}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The {\em $M$-polynomial} of $G$ is introduced with $\displaystyle{M(G;x,y) = \sum_{i\le j} m_{ij}(G)x^iy^j}$.…

Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defined a new graph invariant which is named the Sombor index $\mathrm{SO}(G)$ of a graph $G$ and is computed via the expression \[ \mathrm{SO}(G) = \sum_{u \sim v}…

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…

A new geometric background of graph invariants was introduced by Gutman, of which the simplest is the second Sombor index $SO_2$, defined as $SO_2=SO_2(G)=\sum_{uv\in E}\frac{|d^2_G(u)-d^2_G(v)|}{d^2_G(u)+d^2_G(v)}$, where $G = (V, E)$ is a…