Applying the Diamond Product of Graphs to the Round Robin Tournament Scheduling Problem
Rutjanisarakul, T. and Sumetthapiwat, S.
Corresponding Email: supphakorn.s@cit.kmutnb.ac.th
Received date: 16 December 2023
Accepted date: 30 April 2024
Abstract:
The diamond product of a graph G(V,E) with a graph H(V′,E′) denoted by G⋄H is a graph whose a vertex set V(G⋄H) is a Hom(G,H) and an edge set E(G⋄H)={{f,g}|f,g∈Hom(G,H) and {f(x),g(x)}∈E′, for all x∈V(G)}. A round robin tournament problem involves creating a schedule where each participant plays against every other participant exactly once. This research represents the application of the diamond product of path graph and complete graph to 2n-participants round robin tournament problem. Moreover, the research also represents an algorithm to find a solution of 2n-participants round robin tournament problem.
Keywords: diamond product; homomorphism; graph theory; scheduling problem