The critical group of K_m×P_n

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• 作者：Hao Liang ; Yong-Liang Pan ; Jian Wang
• 关键词：Graph ; Laplacian matrix ; Critical group ; Invariant factor ; Smith normal form ; Tree number
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 June 2008
• 卷：428
• 期：11-12
• 页码：2723-2729
• 文件大小：115 K

摘要

In this paper, we will show that the structure of the critical group of the graph K_m×P_n is Z/tZ(Z/mtZ)^m-2, where , where c4603b16676daad0d7735db7" title="Click to view the MathML source" alt="Click to view the MathML source">x₁ and c4ce397779e60124f8a16d15b0c68" title="Click to view the MathML source" alt="Click to view the MathML source">x₂ are the two roots of the quadratic x²-(m+2)x+1=0.