2024/11/19 by Anjitha Ashokan, Ashokan, Anjitha, A V Chithra +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2411.12599
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The eccentricity matrix of a simple connected graph is derived from its distance matrix by preserving the largest non-zero distance in each row and column, while the other entries are set to zero. This article examines the ε-spectrum, ε-energy, ε-inertia and irreducibility of the central graph (respectively complement of the central graph) of a triangle-free regular graph(respectively regular graph). Also look into the ε-spectrum and the irreducibility of different central graph operations, such as central vertex join, central edge join, and central vertex-edge join. We also examine the ε- energy of some specific graphs. These findings allow us to construct new families of ε-cospectral graphs and non ε-cospectral ε-equienergetic graphs. Additionally, we investigate certain upper and lower bounds for the eccentricity Wiener index of graphs. Also, provide an upper bound for the eccentricity energy of a self-centered graph.