an:06250571
Zbl 1281.05072
Reiner, Victor; Tseng, Dennis
Critical groups of covering, voltage and signed graphs
EN
Discrete Math. 318, 10-40 (2014).
00328630
2014
j
05C22
covering; signed; voltage; critical; sandpile group; crown; functorial; morphism
Summary: Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a particularly pleasant form, leading also to a theory of double covers of signed graphs.