Characterization of commuting graphs of finite groups having small genus

• Date: 2024
• Main Authors: Das, Shrabani, Nongsiang, Deiborlang, Nath, Rajat Kanti
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2024
• Subjects: commuting graph; genus; planar graph; double-toroidal; triple-toroidal; 20D60; 05C25; 05C09
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2211
• Journal Title: Algebra and Discrete Mathematics

In this paper we first show that among all double-toroidal and triple-toroidal finite graphs only \(K_8 \sqcup 9K_1\), \(K_8 \sqcup 5K_2\), \(K_8 \sqcup 3K_4\), \(K_8 \sqcup 9K_3\), \(K_8\sqcup 9(K_1 \vee 3K_2)\), \(3K_6\) and \(3K_6 \sqcup 4K_4 \sqcup 6K_2\) can be realized as commuting graphs of f...