The unicyclic hypergraph with extremal spectral radius

2023/06/28 by Yu, Guanglong, Sun, Lin
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.16027

Abstract

For a hypergraph G=(V, E) consisting of a nonempty vertex set V=V(G) and an edge set E=E(G), its adjacency matrix \mathcal A_G=[(\mathcal A_G)_ij] is defined as (\mathcal A_G)_ij=∑_e∈ E_ij(1)/(|e| - 1), where E_ij = \e ∈ E | i, j ∈ e\.The spectral radius of a hypergraph G, denoted by ρ(\mathcal G), is the maximum modulus among all eigenvalues of \mathcal A_G. In this paper, among all k-uniform (k≥ 3) unicyclic hypergraphs with fixed number of vertices, the hypergraphs with the maximum and the second the maximum spectral radius are completely determined, respectively.

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