On the sign patterns of the smallest signless Laplacian eigenvector

2013/07/29 by Felix Goldberg, Goldberg, Felix, Steve Kirkland +1
Computer Science · Mathematics · #05C50 #15A18 #15B48 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.CO #msc:05C50 #msc:15A18 #msc:15B48

paper · pdf · doi:10.48550/arxiv.1307.7749

arxiv created 2013/07/29 · openalex publication_date 2013/07/29 · arxiv updated 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a connected bipartite graph, whose signless Laplacian matrix is Q(H). Suppose that the bipartition of H is (S,T) and that x is the eigenvector of the smallest eigenvalue of Q(H). It is well-known that x is positive and constant on S, and negative and constant on T. The resilience of the sign pattern of x under addition of edges into the subgraph induced by either S or T is investigated and a number of cases in which the sign pattern of x persists are described.

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