相关论文: Note on Sombor index of connected graphs with give…

Let $d_G(v)$ be the degree of the vertex $v$ in a graph $G$. The Sombor index of $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, which is a new degree-based topological index introduced by Gutman. Let…

Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. The Sombor index of the graph $G$ is a degree-based topological index, defined as $$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$ in which $d(x)$ is the degree of the…

Recently, Gutman defined a new vertex-degree-based graph invariant, named the Sombor index $SO$ of a graph $G$, and is defined by $$SO(G)=\sum_{uv\in E(G)}\sqrt{d_G(u)^2+d_G(v)^2},$$ where $d_G(v)$ is the degree of the vertex $v$ of $G$. In…

In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the…

The general Sombor index of $G$ is defined as $SO_{\alpha}(G)= \sum_{uv\in G}\left(d^2_{G}(u)+d^2_{G}(v)\right)^{\alpha}$. For $0<\alpha<1$, we have the upper bound of $SO_{\alpha}(G)$ on unicyclic graphs with a fixed diameter, and the…

Let $G=(V,E)$ be a finite simple graph. The Sombor index $SO(G)$ of $G$ is defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2}$, where $d_u$ is the degree of vertex $u$ in $G$. In this paper, we study this index for certain graphs and we…

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,…

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…

Let $G=(V,E)$ be a finite simple graph. The Sombor index $SO(G)$ of $G$ is defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2}$, where $d_u$ is the degree of vertex $u$ in $G$. Let $G$ be a connected graph constructed from pairwise disjoint…

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 is one of the geometry-based descriptors, which was defined as $$SO(G)=\sum_{uv\in E(G)}\sqrt{d^{2}(u)+d^{2}(v)},$$ where $d(u)$ (resp. $d(v)$) denotes the degree of vertex $u$ (resp. $v$) in $G$. In this note, we determine…

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…

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 $G$.…

The Sombor index is a topological index in graph theory defined by Gutman in 2021. In this article we find the maximum Sombor index of unicyclic graphs with a fixed number of pendant vertices. We also provide the unique graph among the…

In this paper, we investigate the Diminished Sombor index (DSO), a recently introduced degree-based topological index for a simple graph $G$, defined as \[ DSO(G) = \sum_{uv \in E} \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] where $d_u$ denotes…

Recently in 2021, Gutman introduced the Sombor index of a graph, a novel degree-based topological index. It has been shown that the Sombor index efficiently models the thermodynamic properties of chemical compounds. Assume $\mathbb{B}_n^k$…

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}…

Let $G$ be a connected graph having more than two vertices and let $d_i$ denote the degree of vertex $v_i$ in $G$. Let $E(G)$ represent the edge set of $G$. Then, the augmented Sombor (ASO) index of $G$ is defined as $ASO(G) = \sum_{v_i v_j…

We introduce a degree-based variable topological index inspired on the power (or generalized) mean. We name this new index as the mean Sombor index: $mSO_\alpha(G) = \sum_{uv \in E(G)} \left[\left( d_u^\alpha+d_v^\alpha \right) /2…

The Sombor index of a graph $G$ was recently introduced by Gutman from the geometric point of view, defined as $SO(G)=\sum_{uv\in E(G)}\sqrt{d(u)^2+d(v)^2}$, where $d(u)$ is the degree of a vertex $u$. For two real numbers $\alpha$ and…