Characterizing Powers of Cycles that are Divisor Graphs

Abstract

It was conjectured in a recently published paper that for any integer \(k \geq 8\) and any even integer \(n\) with \(2k+3 < n < 2k+\lfloor\frac{k}{2}\rfloor+3\), the \(k\)th power \(C_n^k\) of the \(n\)-cycle is not a divisor graph. In this paper, we prove this conjecture, hence obtaining a complete characterization of those powers of cycles which are divisor graphs.