Entire Sombor Index of Graphs

Document Type : Research Paper


1 Golestan University

2 Islamic Azad University


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 vertex $x \in V$ for $x=u, v$. \\
In this paper, we introduce a new topological index called the entire Sombor index of a graph which is defined as the sum of the terms $\sqrt{d(x)^2+d(y)^2}$ where $x$ is either adjacent or incident to $y$ and $x, y \in V \cup E$. We obtain exact values of this new topological index in some graphs families. Some important properties of this index are obtained.


Main Subjects

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