Unramified Graph Covers of Finite Degree

Hau Wen Huang, Wen Ching Winnie Li

Research output: Chapter in Book/Report/Conference proceedingChapter


Regarding the fundamental group of a finite connected undirected graph X as the absolute Galois group of X, in this chapter we explore graph theoretical counterparts of several important theorems for number fields. We first characterize finite-degree unramified normal covers of X for which the Chebotarëv density theorem holds in natural density. Then we give finite necessary and sufficient conditions to classify finite-degree unramified covers of X up to equivalence. Similar to the reciprocity law for finite Galois extensions of a number field, it is shown that the unramified normal covers of X of degree d, up to isomorphism, are determined by the primes of X of length ≤ (4|X| - 1)d - 1 which split completely. Finally we obtain a finite criterion for Sunada equivalence, improving a result of Somodi.

Original languageEnglish (US)
Title of host publicationConnections in Discrete Mathematics
Subtitle of host publicationA Celebration of the Work of Ron Graham
PublisherCambridge University Press
Number of pages21
ISBN (Electronic)9781316650295
ISBN (Print)9781107153981
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics


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