Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 1 2026 03 01 Characterization of some finite groups by prime order element graph 81 85 2550 10.22061/jdma.2025.12206.1142 EN Zahra Momen Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, I. R. Iran. Journal Article 2025 07 02 For a finite group <em>G</em>, the prime order element graph of <em>G</em>, is defined as follows: the vertex set is the elements of <em>G</em> and two distinct vertices <em>a</em> and <em>b</em> are adjacent if and only if order of <em>ab</em> is prime. This graph is denoted by <em>γ</em>(<em>G</em>). In this paper, we prove that the alternating groups <em>A</em>₄ and <em>A</em>₅, all groups of order <em>pq</em>, where <em>p</em> and <em>q</em> are prime numbers, and cyclic groups <em>Z_p</em> of prime order are uniquely characterized by the prime order element graph. https://jdma.sru.ac.ir/article_2550_142077533237eb8b10bca960b052d0e0.pdf