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