Distance two labellings for 8-regular grid. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Kim, Byeong Moon; Song, Byung Chul
• Is Part Of: International journal of computer mathematics. Volume 3:Issue 4(2018)
• Page Start: 274
• Page End: 280
• Publication Date: 2018-10-02
• Subjects: -labelling -- 8-regular grid -- octagonal grid -- channel assignment problem -- wireless network -- strong product; 05C15 -- 05C78 -- 05C38; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2018.1545702
• Languages: English
• ISSNs: 2379-9927

Abstract

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 .