Distance two labellings for 8-regular grid. Issue 4 (2nd October 2018) - Kim, Byeong Moon; Song, Byung Chul
ABSTRACT: An -labelling of a graph is a function f on V such that if and if . The span of f is the difference between the maximum and the minimum of f . The -labelling number of G is the minimum span over all -labellings of G . Calamoneri et al. [ New bounds for the number of regular grids, Int. J. Mobile Netw. Design Innovat. 1 (2006), pp. 92–101] found lower bounds and upper bounds of for all h and k when and G is the 8-regular grid . In this paper, we obtain lower bounds and upper bounds of when h < k . Also we improve the result of Calamoneri when .