Related papers: On the first Banhatti-Sombor index

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 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…

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 Hyperbolic Sombor index $HSO(G)$ of a graph $G$ is defined as \begin{align*} HSO(G) = \sum_{v_iv_j \in E(G)} \frac{\sqrt{d_i^{2}+d_j^{2}}}{\min\{d_i,d_j\}}, \end{align*} where $d_i$ and $d_j$ denote the degrees of the vertices $v_i$ 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…

For a simple connected graph $G=(V,E)$, let $d(u)$ be the degree of the vertex $u$ of $G$. The general Sombor index of $G$ is defined as $$SO_{\alpha}(G)=\sum_{uv\in E} \left[d(u)^2+d(v)^2\right]^\alpha$$ where $SO(G)=SO_{0.5}(G)$ is the…

The diminished Sombor index $(DSO)$ of a graph $G$, introduced by Rajathagiri, is defined as $$DSO(G)=\sum_{uv\in E}\frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v},$$ where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v$. A graph $G$ is a…

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,…

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…

Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, where $d_{u}$ denotes the degree of vertex $u$. In this paper, we first determine the…

Let $G$ be a simple connected graph with the vertex set $V(G)$ and $d_{B}^2(u,v)$ be the biharmonic distance between two vertices $u$ and $v$ in $G$. The biharmonic index $BH(G)$ of $G$ is defined as $$BH(G)=\frac{1}{2}\sum\limits_{u\in…

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…

The Sombor index (SO) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of $\sqrt{d_i^2+d_j^2}$, where $d_i$ is the degree of the $i$-th vertex. It has been conceived using geometric…

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 $G$.…

Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $\varphi$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{\varphi(d_u^+,d_v^-)}$,…

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…

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,…

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…