Spectral properties of p-Sombor matrices and beyond

Let $G=(V(G),E(G))$ be a simple graph with vertex set $V(G)=\{v_{1},v_{2},\cdots, v_{n}\}$ and edge $E(G)$. The $p$-Sombor matrix $\mathcal{S}_{p}(G)$ of $G$ is the square order $n$ whose $(i,j)$-entry equal to $((d_{i})^{p}+(d_{j})^{p})^{\frac{1}{p}}$ if $v_{i}\sim v_{j}$, 0 otherwise, where $d_{i}$ denotes degree $v_{i}$ in $G$. In this paper, we study relationship between index $SO_{p}(G)$ by $k$-th spectral moment $N_{k}$ radius $\mathcal{S}_{p}(G)$. Then obtain some bounds Laplacian eigenvalues, radius, spread, energy Estrada index. We also investigate Nordhaus-Gaddum-type results for energy. At last, give regression model boiling point other invariants.