On L? (2, 1)-Edge Coloring Number of Regular Grids

Title

On L? (2, 1)-Edge Coloring Number of Regular Grids

Creator

Deepthy D.; Kureethara J.V.

Description

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. 2019 D. Deepthy et al.

Source

Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, Vol-27, No. 3, pp. 65-81.

Date

2019-01-01

Publisher

Sciendo

Subject

critical graph; hexagonal and triangular grids; L? (2,1) edge coloring number; rectangular

Coverage

Deepthy D., Bharathiar University, Coimbatore, India; Kureethara J.V., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 12241784

Format

Online

Language

English

Type

Article

Identifier

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

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