Graphs whose critical groups have larger rank |
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| Authors: | Yao Ping Hou Wai Chee Shiu Wai Hong Chan |
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| Institution: | (1) Department of Mathematics, Jimei University, Xiamen, 361021, P.R. China;(2) Department of Mathematics, Xiamen University, Xiamen, 361005, P.R. China |
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| 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. |
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| Keywords: | Critical group of a graph Laplacian matrix Smith normal form |
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