Purpose

The purpose of this paper is to assess the application of graph coloring and domination to solve the airline-scheduling problem. Graph coloring and domination in graphs have plenty of applications in computer, communication, biological, social, air traffic flow network and airline scheduling.

Design/methodology/approach

The process of merging the concept of graph node coloring and domination is called the dominator coloring or the χ_d coloring of a graph, which is defined as a proper coloring of nodes in which each node of the graph dominates all nodes of at least one-color class.

Findings

The smallest number of colors used in dominator coloring of a graph is called the dominator coloring number of the graph. The dominator coloring of line graph, central graph, middle graph and total graph of some generalized Petersen graph P_(n ,1) is obtained and the relation between them is established.

Originality/value

The dominator coloring number of certain graph is obtained and the association between the dominator coloring number and domination number of it is established in this paper.

中文翻译：

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用于空中交通和空中调度管理应用的某些图形着色的分析建模

目的

本文的目的是评估图着色和支配在解决航空公司调度问题中的应用。图着色和图支配在计算机、通信、生物、社会、空中交通流量网络和航空公司调度中有大量应用。

设计/方法/方法

将图节点着色和支配概念合并的过程称为图的支配者着色或χ_d着色，定义为图的每个节点支配至少一种颜色的所有节点的节点的适当着色班级。

发现

图形的支配着色中使用的最小颜色数称为图形的支配着色数。得到了一些广义Petersen图P_(n ,1)的折线图、中心图、中间图和全图的支配着色，并建立了它们之间的关系。

原创性/价值

得到某图的支配着色数，并建立支配着色数与其支配数之间的关联。