- School of Mathematics and Statistics - Research Publications
School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableCubic graphical regular representations of Ree groupsFang, T ; Xia, B ; Zheng, S ; Zhou, S (TAYLOR & FRANCIS INC, 2023-09-02)
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ItemNo Preview AvailableA Graph Symmetrization Bound on Channel Information Leakage Under Blowfish PrivacyEdwards, T ; Rubinstein, BIP ; Zhang, Z ; Zhou, S (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2022-01)
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ItemHamiltonicity of 3-Arc GraphsXu, G ; Zhou, S (SPRINGER JAPAN KK, 2014-09)
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ItemThe L(2,1)-labelling problem for cubic Cayley graphs on dihedral groupsLi, X ; Mak-Hau, V ; Zhou, S (SPRINGER, 2013-05)
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ItemUnitary graphs and classification of a family of symmetric graphs with complete quotientsGiulietti, M ; Marcugini, S ; Pambianco, F ; Zhou, S (SPRINGER, 2013-11)
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ItemCanonical double covers of generalized Petersen graphs, and double generalized Petersen graphsQin, Y-L ; Xia, B ; Zhou, S (WILEY, 2021-05)Abstract The canonical double cover of a graph is the direct product of and . If then is called stable; otherwise is called unstable. An unstable graph is said to be nontrivially unstable if it is connected, non‐bipartite and no two vertices have the same neighborhood. In 2008 Wilson conjectured that, if the generalized Petersen graph is nontrivially unstable, then both and are even, and either is odd and , or . In this note we prove that this conjecture is true. At the same time we determine all possible isomorphisms among the generalized Petersen graphs, the canonical double covers of the generalized Petersen graphs, and the double generalized Petersen graphs. Based on these we completely determine the full automorphism group of the canonical double cover of for any pair of integers with .
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ItemForwarding and optical indices of 4-regular circulant networksGan, H-S ; Mokhtar, H ; Zhou, S (ELSEVIER SCIENCE BV, 2015-11)
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ItemBounding the bandwidths for graphsZhou, SM (ELSEVIER SCIENCE BV, 2000-10-28)
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ItemFROBENIUS CIRCULANT GRAPHS OF VALENCY FOURThomson, A ; Zhou, S (CAMBRIDGE UNIV PRESS, 2008-10)Abstract A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group $K \rtimes H$ such that S=aH for some a∈K with 〈aH〉=K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4-valent circulant graph with a given diameter and maximum possible order.
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ItemLabelling Cayley graphs on Abelian groupsZhou, SM (SIAM PUBLICATIONS, 2006)