On the decycling of powers and products of cycles

TL;DR

This paper determines the exact decycling numbers for specific graph products involving cycles, providing precise values for certain cases like the Cartesian product of cycles and powers of cycles.

Contribution

It offers exact decycling numbers for $C_{m} imes C_{n}$ with $m=3,4$, and for powers $C_{n}^{2}$ and $C_{n}^{3}$, advancing understanding of cycle graph decycling.

Findings

Exact decycling numbers for $C_{m} imes C_{n}$ when $m=3,4$

Exact decycling numbers for $C_{n}^{2}$ and $C_{n}^{3}$

Provides formulas and methods for calculating decycling numbers in these cases

Abstract

We calculate exact values of the decycling numbers of $C_{m} \times C_{n}$ for $m=3,4$, of $C_{n}^{2}$, and of $C_{n}^{3}$.