On Euler-Sombor Energy of Graphs

Sopan Bansode; Sharad Barde; Ganesh Mundhe

paper

On Euler-Sombor Energy of Graphs

arXiv:2502.08304

Abstract

In 2024, Gutman et al. \cite{I.Gutman 3} defined a new molecular descriptor called as The Euler-Sombor $(E S)$ index of graph. By using this index we define the Euler-Sombor $(E S)$ matrix of a graph $G$ whoes $(i, j)^{t h}$ entry is $d_{i}^{2} + d_{j}^{2} + d_{i} . d_{j}$ if vertex $v_{i}$ is adjacent to vertex $v_{j}$ , otherwise $0$ . The $E S$ eigenvalues of the graph $G$ are the eigenvalues of its $E S$ matrix , $E S (G)$ . In this paper we discus $E S$ eigenvalues $ν_{i}$ and energy of some classes of graphs.