The least eigenvalues of integral circulant graphs

2023/11/15 by Basic, Milan
#05C50 05C35 11A25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.09120

Abstract

The integral circulant graph ICG_n (D) has the vertex set Z_n = \0, 1, 2, …, n - 1\, where vertices a and b are adjacent if gcd(a-b,n)∈ D, with D ⊆ \d : d | n, 1≤ d1 or not, respectively. In all the aforementioned tasks, we provide a complete characterization of graphs whose spectra contain these determined minimal least eigenvalues.

Related

• Integral mixed circulant graph
• The least eigenvalue of the complements of graphs with given connectivity
• A note on an infinite family of graphs with all different integral Laplacian eigenvalues
• The least signless Laplacian eigenvalue of the complements of bicyclic\n graphs
• Integral cographs and applications