On irreducibility of eccentricity matrix of graphs and construction of ε-equienergetic graphs

2024/04/30 by Anjitha Ashokan, Ashokan, Anjitha, A. V. Chithra +1
Computer Science · Mathematics · #05C50 #05C76 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.19537

openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The eccentricity matrix ε(G), of a connected graph G is obtained by retaining the maximum distance from each row and column of the distance matrix of G and the other entries are assigned with 0. In this paper, we discuss the eccentricity spectrum of subdivision vertex (edge) join of regular graphs. Also, we obtain new families of graphs having irreducible or reducible eccentricity matrix. Furthermore, we use these results to construct infinitely many ε-cospectral graph pairs as well as infinitely many pairs and triplets of ε-cospectral ε-equienergetic graphs. Moreover, we present some new family of ε-integral graphs.

Related

• Eccentricity spectrum of join of central graphs and Eccentricity Wiener index of graphs
• On the spectral radius and the energy of eccentricity matrix of a graph
• Eccentricity spectral properties of C-graphs
• On the graphs having at most one positive eccentricity eigenvalue
• Connected graphs with large multiplicity of -1 in the spectrum of the eccentricity matrix