On 2-arc-transitive graphs of product action type
Zai Ping Lu
TL;DR
This paper investigates the structure of 2-arc-transitive graphs of product action type, establishing restrictions on their parameters and providing new constructions for both bipartite and non-diagonal cases.
Contribution
It introduces new restrictions on vertex-stabilizers and valency, and offers novel constructions for 2-arc-transitive graphs of product action type, expanding the known families.
Findings
Restrictions on vertex-stabilizers and valency for such graphs
Construction methods using equidistant linear codes
New families of 2-arc-transitive graphs of product action type
Abstract
In this paper, we discuss the structural information about 2-arc-transitive (non-bipartite and bipartite) graphs of product action type. It is proved that a 2-arc-transitive graph of product action type requires certain restrictions on either the vertex-stabilizers or the valency. Based on the existence of some equidistant linear codes, a construction is given for 2-arc-transitive graphs of non-diagonal product action type, which produces several families of such graphs. Besides, a nontrivial construction is given for 2-arc-transitive bipartite graphs of diagonal product action type
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research