A construction of imprimitive symmetric graphs which are not multicovers of their quotients

TL;DR

This paper establishes a precise condition for the existence of certain symmetric graphs that are imprimitive and not simple multicover extensions of their quotient graphs, advancing understanding in algebraic graph theory.

Contribution

It provides a necessary and sufficient condition for the existence of (X, s)-arc-transitive imprimitive graphs that are not multicover of their quotients.

Findings

Characterizes when such graphs exist.

Identifies conditions that distinguish these graphs from multicover structures.

Enhances classification of symmetric graphs with imprimitive automorphism groups.

Abstract

This paper gives a sufficient and necessary condition for the existence of an (X, s)-arc-transitive imprimitive graph which is not a multicover of a given quotient graph.