Author(s)

Xiujun Zhang^1,2, Hong Yang², Hong Li²

¹School of Information Science and Engineering, Chengdu University, Chengdu, China.
²Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu, China.

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.

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

Zhang, X. , Yang, H. and Li, H. (2017) L(2,1)-Labeling of the Brick Product Graphs. Journal of Applied Mathematics and Physics, 5, 1529-1536. doi: 10.4236/jamp.2017.58126.