Orbits on vertices and edges of finite graphs
type: Item
instance of: scholarly article
title: Orbits on vertices and edges of finite graphs
zbMATH Open document ID: 0587.05030
DOI: 10.1016/0012-365X(85)90181-5
author: Dominique Buset
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let \(P\) be the set of all ordered pairs \((v,\varepsilon)\) of integers, \(v>0\), \(\varepsilon \geq 0\), for which there exists a finite graph whose automorphism group has exactly \(v\) orbits on the set of vertices and \(\varepsilon\) orbits on the set of edges. Let \(P_c\) be the analogous set for connected graphs. Theorem 1. \((v,\varepsilon)\in P\) iff \(v\leq 2\varepsilon +1\). Theorem 2. \((v,\varepsilon)\in P_c\) iff \(v\leq \varepsilon +1\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 3941570
zbMATH Keywords: orbits of the automorphism group
reviewed by: Regina Iosifovna Tyshkevich
MaRDI profile type: Publication
cites work: Automorphism groups of graphs
description: scientific article; zbMATH DE number 3941570