Analytical modeling on the coloring of certain graphs for applications of air traffic and air scheduling management
Aircraft Engineering and Aerospace Technology
ISSN: 0002-2667
Article publication date: 4 August 2021
Issue publication date: 23 March 2022
Abstract
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.
Keywords
Citation
T., M., R., R. and T.R., P. (2022), "Analytical modeling on the coloring of certain graphs for applications of air traffic and air scheduling management", Aircraft Engineering and Aerospace Technology, Vol. 94 No. 4, pp. 623-632. https://doi.org/10.1108/AEAT-04-2021-0104
Publisher
:Emerald Publishing Limited
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