INDUCED \(nK_{2}\) DECOMPOSITION OF INFINITE SQUARE GRIDS AND INFINITE HEXAGONAL GRIDS

Abstract

The induced \(nK_2\) decomposition of infinite square grids and hexagonal grids are described here. We use the multi-level distance edge labeling as an effective technique in the decomposition of square grids. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. Only non-negative integers are used for labeling. The proposed partitioning technique per the edge labels to get the induced \(nK_2\) decomposition of the ladder graph is the square grid and the hexagonal grid.

Keywords

• distance labelling, channel assignment, \(l(h,k)\)-colouring, rectangular grid, hexagonal grid.