Enumeration of cospectral and coinvariant graphs
作者：
Highlights：
• Enumeration on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (cospectral mate), or at least one other graph with the same Smith normal form (coinvariant mate).
• The Smith normal form of the distance Laplacian and the signless dis- tance Laplacian matrices could be aner invariant than the spectrum to distinguish graphs.
• New graph characterization using the Smith normal form of the distance signless Laplacian matrix.
摘要
•Enumeration on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (cospectral mate), or at least one other graph with the same Smith normal form (coinvariant mate).•The Smith normal form of the distance Laplacian and the signless dis- tance Laplacian matrices could be aner invariant than the spectrum to distinguish graphs.•New graph characterization using the Smith normal form of the distance signless Laplacian matrix.
论文关键词：Graph invariant,Eigenvalues,Invariant factors,Smith normal form,Enumeration
论文评审过程：Received 28 August 2020, Revised 29 April 2021, Accepted 2 May 2021, Available online 21 May 2021, Version of Record 21 May 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126348
