Algebraic Graph Theory

TL;DR

This paper introduces key concepts and notable examples in algebraic graph theory, emphasizing symmetry, combinatorial structures, and computational methods using SageMath.

Contribution

It provides an overview of algebraic graph theory topics, including constructions, properties, and computational tools for automorphism groups.

Findings

Descriptions of notable graphs like Petersen, Paley, Hamming, and Hoffman-Singleton

Illustrations of symmetry and automorphism group computations

Connections between graphs and permutation groups

Abstract

This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen graph, Paley graphs, Hamming graphs, and the Hoffman-Singleton graph, with emphasis on their symmetry and combinatorial structure. Connections with permutation groups are also discussed. Computational examples using SageMath are included to illustrate key concepts and to compute automorphism groups and related invariants.