## Abstract We investigate the properties of graphs whose automorphism group is the symmetric group. In particular, we characterize graphs on less than 2__n__ points with group __S~n~__, and construct all graphs on __n__ + 3 points with group __S~n~__. Graphs with 2__n__ or more points and group __
Cubic graphs with most automorphisms
✍ Scribed by Rev. Michael A. van Opstall; Răzvan Veliche
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 262 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We give a sharp bound for the order of the automorphism group of a connected simple cubic graph on a given number of vertices. For each number of vertices we construct a graph, unique in special cases, attaining the bound. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 99–115, 2010
📜 SIMILAR VOLUMES
Let 1 be a graph with almost transitive group Aut(1) and quadratic growth. We show that Aut(1) contains an almost transitive subgroup isomorphic to the free abelian group Z 2 .
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a
We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n+O(n / g) < 3n / 10+O(n / g) This research was done when the Petr Škoda was a student of