Application of the local antimagic total labeling of graphs to optimise scheduling system for an expatriate assignment

Abstract

An expatriate assignment at the branch company in other country must be optimised due to the short term duty. Accuracy calculation is needed to optimise the expatriate assignment including its scheduling system. There are many ways and methods to optimise the scheduling system. One of the methods is making use of graph theory instruments such as local antimagic total labeling. The local antimagic total labeling of a graph is a map from the set of vertices and edges of the graph to the set of positive integers from 1 to the number of vertices and edges such that the weight of two adjacent vertices are different. The vertex weight is calculated by adding the labels of the vertex and all edges incident to it. In this paper, this labeling is applied to optimise the scheduling system for the expatriate assignment. This system can be modelled by a graph where the assignments are represented by vertices and connection between the assignments are represented by edges. The represented graph is then labelled by the local antimagic total labeling in order to obtain the minimum number of different vertex weights. The such number is equivalent to the optimal time allocated for the expatriate assignment.