1. On L′ (2, 1)–Edge Coloring Number of Regular Grids
- Author
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Deepthy D. and Kureethara Joseph Varghese
- Subjects
l′ (2,1) edge coloring number ,critical graph ,rectangular ,hexagonal and triangular grids ,primary 05c15 ,secondary 05c63 ,Mathematics ,QA1-939 - Abstract
In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative integers. 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. We find the edge coloring number of these grids to be 9, 7 and 16, respectively so that we could color the edges of a rectangular, hexagonal and triangular grid with at most 10, 8 and 17 colors, respectively using this coloring technique. Repeating the sequence pattern for different grids, we can color the edges of a grid of larger size.
- Published
- 2019
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