Eccentricity spectral properties of C-graphs

2025/09/20 by Ashokan, Anjitha, A, Chithra
#05C50 #05C76 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.16657

Abstract

A cograph is a simple graph that contains no induced path on four vertices. In this paper, we consider C-graphs, which are a specific class of cographs, defined as K_α₁∪ K_α₂∪ ⋯ ∪ K_α_2k, % where k ≥ 2, α_2k≥ 2, where k ≥ 2, α_2k ≥ 2, and K_α_i denotes the complete graph on α_i vertices. We investigate the spectral properties of the eccentricity matrix of this particular class of cographs. Additionally, we determine the irreducibility and inertia of the eccentricity matrix of C-graphs. Furthermore, we identify an interval (-1-√(2),-2)∪ (-2,0) in which these graphs have no eccentricity eigenvalues.

Citations

• Laplacian eigenvalues and eigenspaces of cographs generated by finite sequence
• Eigenvalue location in cographs
• The number of trees in a graph

Related

• Spectral properties of C-graphs
• Inertia and spectral symmetry of eccentricity matrices of some clique trees
• Eccentricity spectrum of join of central graphs and Eccentricity Wiener index of graphs
• On the graphs having at most one positive eccentricity eigenvalue
• On irreducibility of eccentricity matrix of graphs and construction of ε-equienergetic graphs