Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Nordhaus–Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph

Clive Elphick
Mustapha Aouchiche
Journal / Anthology

Linear AlgebraanditsApplications
Year: 2017
Volume: 530
Page range: 150-159

Terpai [21]proved the Nordhaus–Gaddum bound that μ(G) +μ(G) ≤4n/3 −1, where μ(G)is the spectral radius of a graph Gwith nvertices. Let s+denote the sum of the squares of the positive eigenvalues of G. We prove that s+(G)+s+(G)<√2nand conjecture that s+(G)+s+(G)≤4n/3 −1. We have used AutoGraphiX and Wolfram Mathematica to search for a counter-example. We also consider Nordhaus–Gaddum bounds for s+and bounds for the Randić index.

*Mathematics > Algebra
*Mathematics > Algebra > Linear Algebra