Recognition of the symplectic simple group $PS{p}_4(p)$ by the order and degree prime-power graph

Let $G$ be a finite group, $\mathrm{cd}(G)$ the set of all irreducible character degrees of $G$, and $\rho (G)$ the set of all prime divisors of integers in $\mathrm{cd}(G)$. For a prime $p$ and a positive integer $n$, let $n_p$ denote the $p$-part of $n$. The degree prime-power graph of $G$ is a graph whose vertex set is $V(G)=\left\{p^{e_p(G)}\mid p\in \rho (G)\right\}$, where $p^{e_p(G)}=max\left\{n_p\mid n\in \mathrm{cd}(G)\right\}$, and there is an edge between distinct numbers $x,y\in V(G)$ if $xy$ divides some integer in $\mathrm{cd}(G)$. The authors have previously shown that some non-abelian simple groups can be uniquely determined by their orders and degree prime-power graphs. In this paper, the authors build on this work and demonstrate that the symplectic simple group $PS{p}_4(p)$ can be uniquely identified by its order and degree prime-power graph.