Paper Info
Title
Enumeration of Highly Irregular Trees by Automorphism Group.
Abstract
A connected graph is highly irregular if the neighbors of each vertex have distinct degrees. We will show that every highly irregular tree has at most one nontrivial automorphism. The question that motivated tins work concerns the proportion of highly irregular trees that are asymmetric, i.e., have no nontrivial automorphisms. A d-tree is a tree in which every vertex has degree at most d. A technique for enumerating unlabeled highly irregular d-trees by automorphism group will be described for d >= 4 and results will be given for d = 4. It will be shown that, for fixed d, d >= 4, almost all highly irregular d-trees are asymmetric.
Year
Venue
Field
2010
ARS COMBINATORIA
Discrete mathematics,Automorphism group,Combinatorics,Enumeration,Mathematics
DocType
Volume
ISSN
Journal
96
0381-7032
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Kathleen A. McKeon1366.94