Perfect (super) edge-magic crowns

TL;DR

This paper investigates the valences of (super) edge-magic labelings of crown graphs, proving perfection for certain cases and providing bounds related to prime factorization.

Contribution

It establishes that crowns are perfect (super) edge-magic when the cycle length is a product of two distinct odd primes and offers a lower bound on the number of valences based on prime factors.

Findings

Crowns are perfect (super) edge-magic when m=pq with p,q odd primes.

Provides a lower bound for the number of valences based on prime factorization.

Extends understanding of valences in edge-magic labelings of crown graphs.

Abstract

In this paper we continue the study of the valences for (super) edge-magic labelings of crowns $C_{m}\odot \overline K_{n}$ and we prove that the crowns are perfect (super) edge-magic when $m=pq$ where $p$ and $q$ are different odd primes. We also provide a lower bound for the number of different valences of $C_{m}\odot \overline K_{n}$, in terms of the prime factors of $m$.