Double-toroidal and \(1\)-planar non-commuting graph of a group

• Date: 2023
• Main Author: Pezzott, J. C. M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: non-commuting graph; double-toroidal graph; \(1\)-planar graph; isoclinism; 05C25; 05C10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935
• Journal Title: Algebra and Discrete Mathematics

Let \(G\) be a finite non-abelian group and denote by \(Z(G)\) its center. The non-commuting graph of \(G\) on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of \(Z(G)\) in \(G\) and two vertices \(x\) and \(y\) are adjacent whenever \(xy\neq yx...