A finite group attached to the laplacian of a graph

✍ Scribed by Dino J. Lorenzini

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 347 KB
• Volume: 91
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(90)90236-b

✦ Synopsis

Lorenzini, D.J., A finite group attached to the laplacian of a graph, Discrete Mathematics 91 (1991) 277-282. Let F = diag(cp,,

. , r~_, , 0), 91, 1 t . 1 q, ~, , denote the Smith normal form of the laplacian matrix associated to a connected graph G on n vertices. Let h denote the cardinal of the set {i 1 rp, > 1). We show that h is bounded by the number of independent cycles of G and we study some cases where these two integers are equal.