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Bipartite divisor graph for the set of irreducible character degrees | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 6، شماره 4، اسفند 2017، صفحه 41-51 اصل مقاله (223.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21221 | ||
| نویسنده | ||
| Roghayeh Hafezieh* | ||
| GEBZE TECHNICAL UNIV. | ||
| چکیده | ||
| Let $G$ be a finite group. We consider the set of the irreducible complex characters of $G$, namely $Irr(G)$, and the related degree set $cd(G)=\{\chi(1) : \chi\in Irr(G)\}$. Let $\rho(G)$ be the set of all primes which divide some character degree of $G$. In this paper we introduce the bipartite divisor graph for $cd(G)$ as an undirected bipartite graph with vertex set $\rho(G)\cup (cd(G)\setminus\{1\})$, such that an element $p$ of $\rho(G)$ is adjacent to an element $m$ of $cd(G)\setminus\{1\}$ if and only if $p$ divides $m$. We denote this graph simply by $B(G)$. Then by means of combinatorial properties of this graph, we discuss the structure of the group $G$. In particular, we consider the cases where $B(G)$ is a path or a cycle. | ||
| کلیدواژهها | ||
| bipartite divisor graph؛ irreducible character degree؛ path؛ cycle | ||
| مراجع | ||
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