A classification of Ramanujan unitary Cayley graphs

被引：1
|
作者：
Droll, Andrew
机构：
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2010年 / 17卷 / 01期
关键词：
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The unitary Cayley graph on n vertices, X-n, has vertex set Z/nZ, and two vertices a and b are connected by an edge if and only if they differ by a multiplicative unit modulo n, i.e. gcd(a - b,n) = 1. A k-regular graph X is Ramanujan if and only if lambda(X) <= 2 root k - 1 where lambda(X) is the second largest absolute value of the eigenvalues of the adjacency matrix of X. We obtain a complete characterization of the cases in which the unitary Cayley graph X-n is a Ramanujan graph.
引用
收藏
页数：6
相关论文
共 50 条
  • [41] DOMINATION IN GENERALIZED UNIT AND UNITARY CAYLEY GRAPHS OF FINITE RINGS
    Chelvam, T. Tamizh
    Kathirvel, S. Anukumar
    Balamurugan, M.
    [J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2020, 51 (02): : 533 - 556
  • [42] Well-Covered and Cohen–Macaulay Unitary Cayley Graphs
    S. Kiani
    H. R. Maimani
    S. Yassemi
    [J]. Acta Mathematica Hungarica, 2014, 144 : 92 - 98
  • [43] On the genus of generalized unit and unitary Cayley graphs of a commutative ring
    T. Asir
    T. Tamizh Chelvam
    [J]. Acta Mathematica Hungarica, 2014, 142 : 444 - 458
  • [44] On Classification of Extendability of Cayley Graphs on Dicyclic Groups
    Bai, Bing
    Huan, Xiao
    Yu, Qinglin
    [J]. UTILITAS MATHEMATICA, 2011, 85 : 201 - 211
  • [45] Edge colorability of unitary endo-cayley graphs of cyclic groups
    Promsakon, C.
    [J]. Journal of Discrete Mathematical Sciences and Cryptography, 2018, 21 (01): : 191 - 198
  • [46] Unitary Cayley graphs of matrix rings over finite commutative rings
    Rattanakangwanwong, Jitsupat
    Meemark, Yotsanan
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2020, 65
  • [47] On the Nonorientable Genus of the Generalized Unit and Unitary Cayley Graphs of a Commutative Ring
    Khorsandi, Mahdi Reza
    Musawi, Seyed Reza
    [J]. ALGEBRA COLLOQUIUM, 2022, 29 (01) : 167 - 180
  • [48] Unitary Cayley graphs whose Roman domination numbers are at most four
    Chin, A. Y. M.
    Maimani, H. R.
    Pournaki, M. R.
    Sivagami, M.
    Tamizh Chelvam, T.
    [J]. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2022, 19 (01) : 36 - 40
  • [49] Computing Wiener and hyper-Wiener indices of unitary Cayley graphs
    Loghman, Amir
    [J]. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 2012, 3 (02): : 121 - 125
  • [50] VERTEX AND EDGE PADMAKAR-IVAN INDICES OF UNITARY CAYLEY GRAPHS
    Philipose, Roshan Sara
    Balakrishnan, Sarasija Perurkada
    [J]. MISSOURI JOURNAL OF MATHEMATICAL SCIENCES, 2019, 31 (02) : 146 - 151
12345