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Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3


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 GH is a graph whose a vertex set V(GH) is a Hom(G,H) and an edge set E(GH)={{f,g}|f,gHom(G,H) and {f(x),g(x)}E, for all xV(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