A note on the algebraic connectivity of a graph and its complement. Issue 7 (19th May 2021) - Afshari, B.; Akbari, S.
Abstract : For a graph G, let λ 2 ( G ) denote its second smallest Laplacian eigenvalue. It was conjectured that λ 2 ( G ) + λ 2 ( G ¯ ) ≥ 1, where G ¯ is the complement of G . In this paper, it is shown that max λ 2 ( G ), λ 2 ( G ¯ ) ≥ 1 2 .