On Euler-Sombor Energy of Graphs

Abstract: In 2024, Gutman et al. \cite{I.Gutman 3} defined a new molecular descriptor called as The Euler-Sombor $(ES)$ index of graph. By using this index we define the Euler-Sombor $(ES)$ matrix of a graph $G$ whoes $(i,j)^{th}$ entry is $\sqrt{{d_i}^2+{d_j}^2+d_i.d_j}$ if vertex $v_i$ is adjacent to vertex $v_j$, otherwise $0$. The $ES$ eigenvalues of the graph $G$ are the eigenvalues of its $ES$ matrix ,$ES(G)$. In this paper we discus $ES$ eigenvalues $\nu_i$ and energy of some classes of graphs.