The competition numbers of ternary Hamming graphs

TL;DR

This paper derives an explicit formula for the competition numbers of ternary Hamming graphs, advancing understanding of these graph invariants in a specific class of graphs.

Contribution

It provides the first explicit formula for competition numbers of ternary Hamming graphs, extending previous results limited to small parameters.

Findings

Derived an explicit formula for competition numbers of H( n, 3 )

Extended known results to ternary Hamming graphs

Provides a basis for further research in graph competition theory

Abstract

It is known to be a hard problem to compute the competition number k(G) of a graph G in general. Park and Sano [13] gave the exact values of the competition numbers of Hamming graphs H(n,q) if $1 \leq n \leq 3$ or $1 \leq q \leq 2$. In this paper, we give an explicit formula of the competition numbers of ternary Hamming graphs.