<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

On <italic>L</italic><sup>′</sup> (2, 1)–Edge Coloring Number of Regular Grids

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On  (2, 1)–Edge Coloring Number of Regular Grids

In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative...

On L^′ (2, 1)–Edge Coloring Number of Regular Grids

Published Online: Dec 21, 2019

Page range: 65 - 81

Received: Dec 10, 2018

Accepted: Jan 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0034

Keywords
′ (2,1) edge coloring number, critical graph, rectangular, hexagonal and triangular grids

© 2019 D. Deepthy et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On L′ (2, 1)–Edge Coloring Number of Regular Grids

Published Online: Dec 21, 2019

Page range: 65 - 81

Received: Dec 10, 2018

Accepted: Jan 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0034

Keywords′ (2,1) edge coloring number, critical graph, rectangular, hexagonal and triangular grids

© 2019 D. Deepthy et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On L^′ (2, 1)–Edge Coloring Number of Regular Grids

Keywords
′ (2,1) edge coloring number, critical graph, rectangular, hexagonal and triangular grids