Job Assignment Problem Using Union Group Graph Labelling
S G Sarika, P.V Usha kumari · IOP Conference Series Materials Science and Engineering · 2021
Abstract Let SG be the group and SG be a collection of subgroups of SG Then the union group graph of SG is a graph denoted by U(SG) whose vertex set is SG itself and two vertices Li and Lj;i≠ j in SG are adjacent if and only if either Li ⊆ Lj or Lj ⊆ Li for i ≠ j. A graph G is said to be union group graph on SG if U(SG) ≅ G for some collection SG of subgroups of SG . This paper describes a simple union group labelling applied in job assignment problem. The task problem related to union group labelling is one of the fundamental combinatorial problems in the branch of optimization. Key words-union group graph, groups, bipartite graph, job assignment problem