An extension of the star complement technique for regular graphs

Citation

Rowlinson P (2018) An extension of the star complement technique for regular graphs. Linear Algebra and Its Applications, 557, pp. 496-507. https://doi.org/10.1016/j.laa.2018.08.018

Abstract
We extend the means by which a regular graph can sometimes be identified from a star complement. In two applications we determine (i) the regular graphs with a path as a star complement for the eigenvalue 1, (ii) the extremal regular graphs which have another type of tree as a star complement for an eigenvalue ≠ -1,0.

Keywords
Eigenvalue; Regular graph; Star complement; Tree

Journal
Linear Algebra and Its Applications: Volume 557