几类有向图的消色差数

IF 0.6 Q4 MATHEMATICS, APPLIED Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-31 DOI:10.1142/s1793830923500908
S. M. Hegde, Lolita Priya Castelino
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引用次数: 0

摘要

设[公式:见文]是一个有向图,有[公式:见文]顶点和[公式:见文]圆弧。当且仅当对于[公式:见文本]的每个弧[公式:见文本],有序对[公式:见文本]至少出现一次时,一个函数[公式:见文本]被称为[公式:见文本]的完全着色。如果配对[公式:见文]未分配,则[公式:见文]称为[公式:见文]的[公式:见文][公式:见文][公式:见文][公式:见文]。[公式:见文]允许适当完全着色的最大值[公式:见文]称为[公式:见文]的[公式:见文][公式:见文],并用[公式:见文]表示。我们得到了有向图和正则有向图消色差数的上界,并研究了单径有向图、独轮车有向图、循环有向图等有向图的消色差数的上界。
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Achromatic Number of Some Classes of Digraphs
Let [Formula: see text] be a directed graph with [Formula: see text] vertices and [Formula: see text] arcs. A function [Formula: see text] where [Formula: see text] is called a complete coloring of [Formula: see text] if and only if for every arc [Formula: see text] of [Formula: see text], the ordered pair [Formula: see text] appears at least once. If the pair [Formula: see text] is not assigned, then [Formula: see text] is called a [Formula: see text] [Formula: see text] [Formula: see text] of [Formula: see text]. The maximum [Formula: see text] for which [Formula: see text] admits a proper complete coloring is called the [Formula: see text] [Formula: see text] of [Formula: see text] and is denoted by [Formula: see text]. We obtain the upper bound for the achromatic number of digraphs and regular digraphs and investigate the same for some classes of digraphs such as unipath, unicycle, circulant digraphs, etc.
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来源期刊
CiteScore
1.50
自引率
41.70%
发文量
129
期刊最新文献
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