Department/School

Mathematics

Date

6-1-2021

Document Type

Article

Keywords

path-cordial abelian groups, Hovey

Abstract

A labeling of the vertices of a graph by elements of any abelian group A induces a labeling of the edges by summing the labels of their endpoints. Hovey defined the graph G to be A-cordial if it has such a labeling where the vertex labels and the edge labels are both evenly-distributed over A in a technical sense. His conjecture that all trees T are A-cordial for all cyclic groups A remains wide open, despite significant attention. Curiously, there has been very little study of whether Hovey’s conjecture might extend beyond the class of cyclic groups. We initiate this study by analyzing the larger class of finite abelian groups A such that all path graphs are A-cordial. We conjecture a complete characterization of such groups, and establish this conjecture for various infinite families of groups as well as for all groups of small order.

Published in

Australasian Journal of Combinatorics

Citation/Other Information

Patrias, R., & Pechenik, O. (2021). Path-cordial abelian groups. Australasian Journal of Combinatorics, 80:157-166.

Included in

Mathematics Commons

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