2018/01/26 by Allem, Luiz Emilio, Tura, Fernando
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1801.08972
Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for λ≠ -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.