کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11033130 | 1632911 | 2019 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The application of representation theory in directed strongly regular graphs
ترجمه فارسی عنوان
کاربرد نظریه نمایندگی در نمودارهای منظم به طور منظم
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کلمات کلیدی
نمودار مرتب مرتب شده است تئوری نمایندگی، نمایندگی منجر شده، گراف کیلی،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
The concept of directed strongly regular graphs (DSRG) was introduced by Duval in 1988 [3]. In the present paper, we use representation theory of finite groups in order to investigate the directed strongly regular Cayley graphs. We first show that a Cayley graph C(G,S) is not a directed strongly regular graph if S is a union of some conjugate classes of G. This generalizes an earlier result of Leif K. Jørgensen [7] on abelian groups. Secondly, by using induced representations, we have a look at the Cayley graph C(NâθH,N1ÃH1) with N1âN and H1âH, determining its characteristic polynomial and its minimal polynomial. Based on this result, we generalize the semidirect product method of Art M. Duval and Dmitri Iourinski in [4] and obtain a larger family of directed strongly regular graphs. Finally, we construct some directed strongly regular Cayley graphs on dihedral groups, which partially generalize the earlier results of Mikhail Klin, Akihiro Munemasa, Mikhail Muzychuk, and Paul Hermann Zieschang in [8]. By using character theory, we also give the characterization of directed strongly regular Cayley graphs C(Dn,XâªXa) with Xâ©X(â1)=â
.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 161, January 2019, Pages 508-536
Journal: Journal of Combinatorial Theory, Series A - Volume 161, January 2019, Pages 508-536
نویسندگان
Yiqin He, Bicheng Zhang,