2-Geodesic-transitive graphs of order twice a prime power
Jiangmin Pan, Cixuan Wu, Yingnan Zhang, Hanlin Zou
TL;DR
This paper classifies and analyzes 2-geodesic-transitive graphs of order twice an odd prime power, introduces new examples, and provides computational tools for their study.
Contribution
It offers a classification of basic and automorphism-group-specific graphs, along with a reduction theorem and Magma code for further research.
Findings
Classified basic 2-geodesic-transitive graphs of specified order.
Discovered new 2-geodesic-transitive graphs.
Provided Magma code for graph analysis.
Abstract
In this paper, we study 2-geodesic-transitive graphs of order twice an odd prime power. Classifications of corresponding basic graphs and such graphs with almost simple automorphism groups are given, and a reduction theorem for general case is obtained. Certain new 2-geodesic-transitive graphs are found, and a Magma code regarding 2-geodesic-transitive graphs is provided.
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