A linear algorithm for radio k-coloring of powers of paths having small diameters

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2024-08-26 DOI:10.1016/j.jcss.2024.103577

Dipayan Chakraborty , Soumen Nandi , Sagnik Sen , D.K. Supraja

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引用次数: 0

Abstract

The radio k-chromatic number $r c_{k} (G)$ of a graph G is the minimum integer λ such that there exists a function $ϕ : V (G) \to {0, 1, \dots, λ}$ satisfying $| ϕ (u) - ϕ (v) | \geq k + 1 - d (u, v)$ , where $d (u, v)$ denotes the distance between u and v. A considerable amount of attention has been given to find the exact values or providing polynomial time algorithms to determine $r c_{k} (G)$ for several basic graph families such as paths, cycles, trees, and powers of paths, usually for some specific values of k. In this article, we find the exact values of $r c_{k} (G)$ where G is a power of a path with diameter strictly less than k. Our proof readily provides a linear time algorithm for assigning a radio k-coloring of G. Furthermore, our proof technique is a potential tool for solving the same problem for other classes of graphs having “small” diameters.

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小直径路径幂的无线电 k 着色线性算法

图 G 的无线电 k 色度数 rck(G) 是存在函数 ϕ:V(G)→{0,1,⋯,λ} 满足 |ϕ(u)-ϕ(v)|≥k+1-d(u,v) 的最小整数 λ，其中 d(u,v) 表示 u 和 v 之间的距离。对于一些基本图族，如路径、循环、树和路径的幂，通常是针对某些特定的 k 值，人们已经花费了大量精力去寻找它们的精确值或提供多项式时间算法来确定 rck(G)。在本文中，我们找到了 rck(G)的精确值，其中 G 是直径严格小于 k 的路径的幂。我们的证明很容易提供一种线性时间算法，用于为 G 指定无线电 k 着色。

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.