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Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids
Dinesan Deepthya, Joseph Varghese Kureetharab a GITAM University
b CHRIST (Deemed To Be University)
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.
Citation:
Dinesan Deepthy, Joseph Varghese Kureethara, “Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids”, Ural Math. J., 8:1 (2022), 23–33
Linking options:
https://www.mathnet.ru/eng/umj158 https://www.mathnet.ru/eng/umj/v8/i1/p23
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Abstract page: | 56 | Full-text PDF : | 20 | References: | 16 |
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