Abstract
Let G = (V,E) be a connected simple graph. A labeling f: V → ℤ2 induces an edge labeling f*: E → ℤ2 defined by f*(xy) = f(x)+ f(y) for each xy ∈ E. For i ∈ ℤ2, let υ f (i) = |f −1(i)| and e f (i) = |f*−1(i)|. A labeling f is called friendly if |υ f (1) − υ f (0)| ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by i f (G) = e f (1) − e f (0). The set {i f (G) | f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI(G). In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.
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Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications, Macmillan, 1976
Shiu, W. C., Kwong, H.: Full friendly index sets of P 2 × P n. Discrete Math., 308, 3688–3693 (2008)
Shiu, W. C., Ling, M. H.: Extreme Friendly Indices of C m × C n. Congr. Numer., 188, 175–182 (2007)
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Supported by FRG/07-08/II-55 Hong Kong Baptist University
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Shiu, W.C., Ling, M.H. Full friendly index sets of Cartesian products of two cycles. Acta. Math. Sin.-English Ser. 26, 1233–1244 (2010). https://doi.org/10.1007/s10114-010-8517-5
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DOI: https://doi.org/10.1007/s10114-010-8517-5