Sách A classification of Ramanujan unitary Cayley graphs

Thảo luận trong 'Sách Ngoại Ngữ' bắt đầu bởi Thúy Viết Bài, 5/12/13.

  1. Thúy Viết Bài

    Thành viên vàng

    Bài viết:
    198,891
    Được thích:
    173
    Điểm thành tích:
    0
    Xu:
    0Xu
    We have completely characterized which unitary Cayley graphs are Ramanujan. We
    remark that every case of Theorem 1 gives rise to infinite families of Ramanujan graphs
    in this form. As shown by Murty in [Murty (2005)], it is impossible to construct an infinite
    family of k-regular abelian Cayley graphs which are all Ramanujan for any particular k.
    However, finding examples of Ramanujan graphs in the way that we have presented here
    is still of some interest. It is also interesting to remark on some other work that has been
    done on unitary Cayley graphs. Various properties of the graph Xn were determined in
    [Klotz, W. and Sander, T. (2007)], including the chromatic number, the clique number,
    the independence number, the diameter, and the vertex connectivity, in addition to some
    work on the eigenvalues. The energy of Xn was determined and studied independently
    in [Ili´c (2009)] and [Ramaswamy, H.N. and Veena, C.R. (2009)]. It is also interesting to
    note that [Ramaswamy, H.N. and Veena, C.R. (2009)] hints at a new approach to finding
    the eigenvalues of Xn using properties of the graph instead of relying on their expression
    as Ramanujan sums.
     

    Các file đính kèm: