2016/12/08 by Elizandro Max Borba, Sebastián Richter, Borba, Elizandro Max +6
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.CO
paper · pdf · doi:10.48550/arxiv.1612.02643
arxiv created 2016/12/08 · openalex publication_date 2016/12/08 · arxiv updated 2016/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The p-spectral radius of a graph G=(V,E) with adjacency matrix A is defined as λ(p)(G)=max \xTAx : ‖x‖p=1 \. This parameter shows remarkable connections with graph invariants, and has been used to generalize some extremal problems. In this work, we extend this approach to the Laplacian matrix L, and define the p-spectral radius of the Laplacian as μ(p)(G)=max \xTLx : ‖x‖p=1 \. We show that μ(p)(G) relates to invariants such as maximum degree and size of a maximum cut. We also show properties of μ(p)(G) as a function of p, and a upper bound on maxG \colon |V(G)|=n μ(p)(G) in terms of n=|V| for p≥ 2, which is attained if n is even.