Enumeration of labeled Eulerian $3$-cacti

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow

Abstract: $k$-Cactus is a connected graph in which each edge is contained in a maximum of $k$ cycles. We obtain exact and asymptotic formulas for the number of labeled Eulerian $3$-cacti with a given number of vertices.

Keywords: enumeration, labeled graph, Eulerian graph, $3$-cactus, asymptotics

UDC: 519.175.3

MSC: 05C30

DOI: 10.36535/2782-4438-2025-242-41-45