A note on unimodular congruence of the Laplacian matrix of a graph

作者：Liang, Hao; Pan, Yong-Liang^*; Wang, Jian; Xu, Jun-Ming

来源：Linear and Multilinear Algebra, 2010, 58(4): 497-501.

DOI：10.1080/03081080802681500

• graph
• Laplacian matrix
• Smith normal form
• unimodular congruence

Let G be a simple connected graph and L(G) be its Laplacian matrix. In this note, we prove that L(G) is congruent by a unimodular matrix to its Smith normal form if and only if G is a tree.

• 出版日期2010
• 单位中国科学技术大学