Cayley graphs of order 30p are hamiltonian

TL;DR

This paper proves that for any finite group of order 30p, with p prime, all Cayley graphs generated by any set have Hamiltonian cycles, confirming a broad Hamiltonian property.

Contribution

It establishes that Cayley graphs of groups of order 30p are Hamiltonian for any generating set, extending known results to this specific class of groups.

Findings

All Cayley graphs of groups of order 30p are Hamiltonian.

Hamiltonian cycles exist in Cayley graphs for any generating set.

The result applies to all primes p and confirms a conjecture for this group order.

Abstract

Suppose G is a finite group of order 30p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).