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Title: On optimal orientation of cycle vertex multiplications
Authors: Ng, K.L. 
Koh, K.M. 
Keywords: Cycle
Orientation number
Strong orientation
Vertex multiplication
Issue Date: 28-Jul-2005
Citation: Ng, K.L., Koh, K.M. (2005-07-28). On optimal orientation of cycle vertex multiplications. Discrete Mathematics 297 (1-3) : 104-118. ScholarBank@NUS Repository.
Abstract: For a bridgeless connected graph G, let D(G) be the family of its strong orientations; and for any D∈D(G), we denote by d(D) its diameter. The orientation number d→(G) of G is defined by d→(G)=min{d(D)|D∈D(G)}. For a connected graph G of order n and for any sequence of n positive integers (si), let G(s1,s2,...,sn) denote the graph with vertex set V* and edge set E* such that V*=∪i=1nVi, where Vi's are pairwise disjoint sets with |Vi|=si, i=1,2,...,n, and for any two distinct vertices x, y in V*, xy∈E* if and only if x∈Vi and y∈Vj for some i,j∈{1,2,...,n} with i≠j such that vivj∈E(G). We call the graph G(s1,s2,...,sn) a G vertex multiplication. In this paper, we determine the orientation numbers of various cycle vertex multiplications. © 2005 Elsevier B.V. All rights reserved.
Source Title: Discrete Mathematics
ISSN: 0012365X
DOI: 10.1016/j.disc.2005.04.012
Appears in Collections:Staff Publications

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