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: [email protected]
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 $G\diamond H$ is a graph whose a vertex set $V(G\diamond H)$ is a $Hom(G,H)$ and an edge set $E(G\diamond H) = \left\{ \{f,g\} | f,g \in Hom(G,H) \right.$ and $\{f(x),g(x)\}\in E',$ for all $\left. x \in V(G) \right\}$. 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
