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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/27952

    Title: Mutually independent hamiltonian cycles for the pancake graphs and the star graphs
    Authors: Lin,CK;Tan,JJM;Huang,HM;Hsu,DF;Hsu,LH
    Contributors: 數學研究所
    Date: 2009
    Issue Date: 2010-06-29 19:38:45 (UTC+8)
    Publisher: 中央大學
    Abstract: A hamiltonian cycle C of a graph G is an ordered set < u(1), u(2,) ..., u(n(G)), u(1)> of vertices such that u(i) not equal u(j) for i not equal j and u(i) is adjacent to u(i+1) for every i is an element of {1, 2, ..., n(G) - 1} and u(n(G)) is adjacent to u(1), where n(G) is the order of G. The vertex u(1) is the starting vertex and u(i) is the ith vertex of C. Two hamiltonian cycles C-1 = < u(1), u(2), ..., u(n(G)), u(1)> and C-2 = < v(1), v(2), ..., v(n(G)), v(1)> of G are independent if u(1) = v(1) and u(i) not equal v(i) for every i is an element of {2, 3, ..., n(G)}. A set of hamiltonian cycles {C-1, C-2, ..., C-k} of G is mutually independent if its elements are pairwise independent. The mutually independent hamiltonicity IHC(G) of a graph G is the maximum integer k such that for any vertex u of G there exist k mutually independent hamiltonian cycles of G starting at u. In this paper, the mutually independent hamiltonicity is considered for two families of Cayley graphs, the n-dimensional pancake graphs P-n and the n-dimensional star graphs S-n. It is proven that IHC(P-3) = 1, IHC(P-n) = n - 1 if n >= 4, IHC(S-n) = n - 2 if n is an element of {3, 4} and IHC(S-n) = n - 1 if n >= 5. (C) 2009 Elsevier B.V. All rights reserved.
    Appears in Collections:[數學研究所] 期刊論文

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