Eulerian character degree graphs of solvable groups

• 出版年: AKCE International Journal of Graphs and Combinatorics
• 主要な著者: G. Sivanesan, C. Selvaraj, T. Tamizh Chelvam
• フォーマット: 論文
• 言語: 英語
• 出版事項: Taylor & Francis Group 2024-05-01
• 主題: Character graph; Eulerian graph; regular graph; finite solvable group; 05C45; 20C15
• オンライン･アクセス: https://www.tandfonline.com/doi/10.1080/09728600.2024.2309620

Let G be a finite group, let Irr(G) be the set of all complex irreducible characters of G and let cd(G) be the set of all degrees of characters in [Formula: see text] Let [Formula: see text] be the set of all primes that divide some degrees in [Formula: see text] The character degree graph [Formula: see text] of G is the simple undirected graph with vertex set [Formula: see text] and in which two distinct vertices p and q are adjacent if there exists a character degree [Formula: see text] such that r is divisible by the product pq. In this paper we obtain a necessary condition for the character degree graph [Formula: see text] of a solvable group G to be eulerian. We also prove that every n – 2 regular graph on n vertices where n is even and [Formula: see text] is the character degree graph of some solvable group. In the last part of the paper we give a bound for the number of Eulerian character degree graphs in terms of number of vertices.