فهرست نشریات علمی دسترسی آزاد ایران

Let $ G $ be a finite simple graph. The Sombor index of $ G $ is defined as $ \sum\nolimits_{uv\in E(G)} \sqrt{d_{u}^{2}+d_{v}^{2}} $ where $d_{u}$ and $d_{v}$ represent the degrees of vertices $ u$ and $v$ in $ G $, respectively. The sum of the absolute values of the adjacency eigenvalues defines the energy of a graph. This paper aims to enhance the current connections between the Sombor index and the energy of graphs. Additionally, we provide some upper bounds for the Sombor index of triangle-free, square-free, $K_r$-free and tripartite graphs in terms of order, size and minimum degree.