@article{Qin2024, 
author = {Chao Qin and Yu Li and Zhongbi Wang and Guiyun Chen},
title = {Recognition of the symplectic simple group    P  S      p    4    (  p  ) by the order and degree prime-power graph},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {2808-2823},
keywords = {degree prime-power graph, irreducible character, degree, maximal p-part, simple group, subnormal series},
url = {https://www.sciopen.com/article/10.3934/math.2024139},
doi = {10.3934/math.2024139},
abstract = {Let    G be a finite group,    cd  ⁡  (  G  ) the set of all irreducible character degrees of    G, and    ρ  (  G  ) the set of all prime divisors of integers in    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  )  =      {                  p                              e            p                    (          G          )                    ∣      p      ∈      ρ      (      G      )        }  , where        p                  e        p            (      G      )        =  max      {                  n        p            ∣      n      ∈      cd      ⁡      (      G      )        }  , and there is an edge between distinct numbers    x  ,  y  ∈  V  (  G  ) if    x  y divides some integer in    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    P  S      p    4    (  p  ) can be uniquely identified by its order and degree prime-power graph.}
}