Elsevier

Discrete Mathematics

Volume 309, Issue 1, 6 January 2009, Pages 255-258
Discrete Mathematics

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Critical groups for homeomorphism classes of graphs

https://doi.org/10.1016/j.disc.2007.12.048Get rights and content
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Abstract

In this paper the weighted fundamental circuits intersection matrix of an edge-labeled graph is introduced for computing the critical groups for homeomorphism classes of graphs. As an application, it is proved that for any given finite connected simple graph there is a homeomorphic graph with cyclic critical group.

Keywords

Critical group
Laplacian matrix
Homeomorphism class
Cyclic group

Cited by (0)

1

The author is supported by National Natural Science Foundation of China (Project 10526016), Development Program for Outstanding Young Teachers in Harbin Institute of Technology (Project HIT.2006.54) and Science Research Foundation in Harbin Institute of Technology (Project HITC2007001).