Locally 3‐Transitive Graphs of Girth 4

Abstract

A natural topic of algebraic graph theory is the study of vertex transitive graphs. In the present article, we investigate locally 3‐transitive graphs of girth 4. Taking our former results on locally symmetric graphs of girth 4 as a starting point, we show what properties are retained if we weaken the requirement of local symmetry to local 3‐transitivity.

Cubic vertex-transitive graphs of girth six

“…The structure of cubic arc-transitive graphs of girth at most 7 and 9 was studied in [8] and [3], respectively, and those of girth 6 were completely determined in [17]. By requiring more symmetry, some of these results can be pushed further; for example, in [19], cubic 4-arc-transitive graphs of girth at most 13 were classified, while in [20], locally 3-transitive graphs of girth 4 are considered. Recently, two papers appeared where the condition on arc-transitivity was relaxed (considerably!)…”