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Peer reviewed
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Zhou, Haiying; Shiu, Wai Chee; Lam, Peter Che Bor
Journal of combinatorial optimization, 10/2014, Volume: 28, Issue: 3Journal Article
Suppose is a positive integer. An -labeling of a simple graph is a function such that if ; and if . The span of an -labeling is the absolute difference between the maximum and minimum labels. The -labeling number, , is the minimum of span over all -labelings of . Whittlesey et al. proved that where and . As a consequence, for . In particular, . In this paper, we provide an elementary proof of this bound. Also, we study the -labeling number of . A lower bound on are provided and are determined.
