4 papers
A generalization of Zhu's theorem on six-valent integer distance graphs
Jonathan Cervantes, Mike Krebs
Given a set of positive integers, the integer distance graph for has the set of integers as its vertex set, where two vertices are adjacent if and only if the absolute valu…
An alternate proof of Payan's theorem on cubelike graphs
Jonathan Cervantes, Mike Krebs
A cubelike graph is a Cayley graph on the product of the integers modulo with itself finitely many times. In 1992, Payan proved tha…
Chromatic numbers of Cayley graphs of abelian groups: Cases of small dimension and rank
Jonathan Cervantes, Mike Krebs
A connected Cayley graph on an abelian group with a finite generating set can be represented by its Heuberger matrix, i.e., an integer matrix whose columns generate the group o…
Chromatic numbers of Cayley graphs of abelian groups: A matrix method
Jonathan Cervantes, Mike Krebs
In this paper, we take a modest first step towards a systematic study of chromatic numbers of Cayley graphs on abelian groups. We lose little when we consider these graphs only whe…