The smallest normalized signless ∞-Laplacian eigenvalue for non-bipartite connected graphs

2024/12/29 by Dai, Yi
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.20513

Abstract

In this paper, we aim to study the smallest normalized signless ∞-Laplacian eigenvalue μ_∞, a generalisation of the smallest signless Laplacian eigenvalue. For a non-bipartite connected graph, we show that the invariant μ_∞ equals to the reciprocal of the minimal ∞-norm of the generalized inverses of the weighted signless incidence matrix. An example is also given to illustrate the result.

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