A characterization of tetravalent half-arc-transitive graphs of girth 5Šparl, Primož (Avtor) Zhou, Jin-Xin (Avtor) Tetravalent graphHalf-arc-transitiveGirth 5A graph is said to be half-arc-transitive if its automorphismgroup is transitive on the vertices and the edges of the graph but not on its arcs. Tetravalent half-arc-transitive graphsof girth 3 were characterized by Marušič and Xu in 1997,while those of girth 4 were characterized by Marušič and Nedela in 2002 and by Potočnik and Wilson in 2007. The investigation of tetravalent half-arc-transitive graphs of girth 5 was initiated by Antončič and Šparl in 2023. In this paper, a characterization of all tetravalent half-arc-transitive graphsof girth 5 is given, and as an application, two open questions from Antončič and Šparl (2023) [1] are answered.20262026-03-10 08:50:35Članek v reviji180459sl