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On the maximum spectral radius of connected graphs with a prescribed order and size | Synapse

June 1, 2026Open Access

On the maximum spectral radius of connected graphs with a prescribed order and size

Key Points

This research aims to maximize the spectral radius of connected simple graphs with a given number of vertices and edges.
Considered connected simple graphs with n vertices and n-1 + e edges.
Focused on cases where e ≤ 130 or n ≥ e + 2 + 13√e.
Analyzed the eigenvalues of the adjacency matrix for these graphs.
Identified optimal conditions for spectral radius in the specified graph sets.
Provided new bounds for spectral radius based on the number of edges and vertices.

Abstract

The spectral radius of a graph is the largest modulus of an eigenvalue of its adjacency matrix. Let C₍, ₄ be the set of all the connected simple graphs with n vertices and n-1 + e edges. Here, we solve the spectral radius maximization problem on C₍, ₄ when e ≤ 130 or n ≥ e + 2 + 13√e.

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Authors

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Ivan Damnjanovic

University of Primorska

Journals

Filomat

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University of Primorska

References and Citations

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Cite this study

Ivan Damnjanovic (Wed,) studied this question.

synapsesocial.com/papers/6a1d228d02fbce91306384ec — DOI: https://doi.org/10.2298/fil2534281d