Further results on the star degree of graphs

作者：

Highlights：

• The computing formula of star degree of a graph is given. And the extramal graphs with SD(G)=n−i are also determined, where i=2;3;4;5.

• The star degree set of n-vertex connected graphs is derived.

• Prove that some graphs with given star degree are determined by their signless Laplacian permanental spectra.

摘要

•The computing formula of star degree of a graph is given. And the extramal graphs with SD(G)=n−i are also determined, where i=2;3;4;5.•The star degree set of n-vertex connected graphs is derived.•Prove that some graphs with given star degree are determined by their signless Laplacian permanental spectra.

论文关键词：Permanent,Permanental root,Star degree,Signless Laplacian permanental spectrum,Signless Laplacian cospectral

论文评审过程：Received 24 January 2022, Revised 2 March 2022, Accepted 5 March 2022, Available online 21 March 2022, Version of Record 21 March 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127076