Analytical modeling on the coloring of certain graphs for applications of air traffic and air scheduling management
T. Manjula, R. Raja Rajeswari, T. R. Praveenkumar · Aircraft Engineering and Aerospace Technology · 2021
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.