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Georges, J.P., Mauro, D.W. and Whittlesey, M.A. (1994) Relating Path Coverings to Vertex Labellings with a Condition at Distance Two. Discrete Mathematics, 135, 103-111.

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• TITLE: L(2,1)-Labeling of the Brick Product Graphs

  AUTHORS: Xiujun Zhang, Hong Yang, Hong Li

  KEYWORDS: Graph Labeling, Brick Product Graph, L((2, 1)-Labeling, Frequency Assignment Problem

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.8, August 23, 2017

  ABSTRACT: A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.