正则网格的L '(2,1) -边着色数

IF 0.8 4区数学 Q2 MATHEMATICS

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2019-12-01 DOI:10.2478/auom-2019-0034

D. Deepthy, J. V. Kureethara

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引用次数: 2

摘要

摘要本文研究了无限矩形、六边形和三角形网格的多级距离边缘标注问题。我们用非负整数标记这些边。如果这两条边是相邻的，那么它们的色差至少是2，如果它们只被一条边分开，那么它们的颜色必须是不同的。我们发现这些网格的边缘上色数分别为9、7和16，因此我们可以使用这种上色技术分别为矩形、六边形和三角形网格的边缘上色最多为10、8和17种颜色。为不同的网格重复序列模式，我们可以为更大尺寸的网格的边缘上色。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is founded by Mirela Stefanescu and Silviu Sburlan in 1993 and is devoted to pure and applied mathematics. Published by Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania.