Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Graphs whose critical groups have larger rank

Language

English

Abstract

The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n - 3 and all graphs with r(G) = β(G) = n - 3 are characterized. © 2011 Springer-Verlag Berlin Heidelberg.

Keywords

Critical group of a graph, Laplacian matrix, Smith normal form

Publication Date

2011

Source Publication Title

Acta Mathematica Sinica

Volume

27

Issue

9

Start Page

1663

End Page

1670

Publisher

Springer Verlag

DOI

10.1007/s10114-011-9358-6

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10114-011-9358-6

ISSN (print)

14398516

ISSN (electronic)

14397617

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