L(p,1)-labelling of graphs
نویسندگان
چکیده
An L(p, 1)-labelling of a graph is a function f from the vertex set to the positive integers such that |f(x) − f(y)| ≥ p if dist(x, y) = 1 and |f(x)− f(y)| ≥ 1 if dist(x, y) = 2, where dist(x, y) is the distance between the two vertices x and y in the graph. The span of an L(p, 1)labelling f is the difference between the largest and the smallest labels used by f plus 1. In 1992, Griggs and Yeh conjectured that every graph with maximum degree ∆ ≥ 2 has an L(2, 1)-labelling with span ∗This work was partially supported by the European project ist fet Aeolus and the Égide eco-net project 16305SB. The first and second author thank the Department of Applied Mathematics kam-dimatia and the Institute for Theoretical Computer Science (iti) of Charles University for their hospitality during their stay in Prague, when part of this research was conducted. The third author was then an Aeolus fellow at iti.
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