A linear algebraic proof of the Laplacian spread conjecture
Abstract
For a graph G, let α(G) denote its second smallest Laplacian eigenvalue. The Laplacian Spread Conjecture is that α(G)+α(G) ≥ 1, where G is the complement of G. In this article, we provide a new proof of the Laplacian spread conjecture by means of linear algebra, which is more concise.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.