Eulerian character degree graphs of solvable groups
| Autor: | G. Sivanesan, C. Selvaraj, T. Tamizh Chelvam |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 21, Iss 2, Pp 161-166 (2024) |
| Druh dokumentu: | article |
| ISSN: | 09728600 2543-3474 0972-8600 |
| DOI: | 10.1080/09728600.2024.2309620 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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