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Nordhaus–Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph
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| Linear AlgebraanditsApplications |
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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.
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