Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 05 26 Finite groups whose commuting graphs are line graphs 14955 10.22049/cco.2025.30252.2384 EN Siddharth Malviy Department of Mathematics, Central University of Rajasthan, Ajmer, India Vipul Kakkar Department of Mathematics, Central University of Rajasthan, Ajmer, India Journal Article 2025 01 07 The commuting graph ${\Gamma(G)}$ of a group $G$ is the simple undirected graph with group elements as a vertex set and two elements $x$ and $y$ are adjacent if and only if $xy=yx$ in $G$. By eliminating the identity element of $G$ and all the dominant vertices of $\Gamma(G)$, the resulting subgraphs of $\Gamma(G)$ are $\Gamma^*(G)$ and $\Gamma^{**}(G)$, respectively. In this paper, we classify all the finite groups $G$ such that the graph $\Delta(G) \in \{\Gamma(G), \Gamma^*(G), \Gamma^{**}(G)\}$ is the line graph of some graph. We also classify all the finite groups $G$ whose graph $\Delta(G) \in \{\Gamma(G), \Gamma^*(G), \Gamma^{**}(G)\}$ is the complement of line graph. https://comb-opt.azaruniv.ac.ir/article_14955_06c90be1232e5f8d5248a964b935760b.pdf