Multiplicity of eigenvalues of cographs

TL;DR

This paper studies the multiplicity of eigenvalues in cographs, especially for balanced cotrees, and introduces new families of borderenergetic cographs with equal energy to complete graphs.

Contribution

It explicitly determines the maximum eigenvalue multiplicity for cographs with balanced cotrees and constructs new non-cospectral, borderenergetic cograph families.

Findings

Maximum eigenvalue multiplicity for balanced cotree cographs identified

Families of non-cospectral borderenergetic cographs constructed

Cographs with eigenvalue multiplicity properties analyzed

Abstract

Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for \lambda \neq -1,0. For cographs with balanced cotrees we determine explicitly the highest value for the multiplicity.The energy of a graph is defined as the sum of absolute values of the eigenvalues. A graph G on n vertices is said to be borderenergetic if its energy equals the energy of the complete graph Kn. We present families of non-cospectral and borderenergetic cographs.