Note: The inverse problem for certain tree parameters

Authors:
íva Czabarka;László Székely;Stephan Wagner
Affiliations:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;Department of Mathematical Sciences, Mathematics Division, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 1

The number of maximal independent sets in a tree

SIAM Journal on Algebraic and Discrete Methods
Bipartite graphs can have any number of independent sets

Discrete Mathematics
Twelve countings with rooted plane trees

European Journal of Combinatorics
Molecular graphs and the inverse Wiener index problem

Discrete Applied Mathematics

Note: Rooted tree statistics from Matula numbers

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

Let p be a graph parameter that assigns a positive integer value to every graph. The inverse problem for p asks for a graph within a prescribed class (here, we will only be concerned with trees), given the value of p. In this context, it is of interest to know whether such a graph can be found for all or at least almost all integer values of p. We will provide a very general setting for this type of problem over the set of all trees, describe some simple examples and finally consider the interesting parameter ''number of subtrees'', where the problem can be reduced to some number-theoretic considerations. Specifically, we will prove that every positive integer, with only 34 exceptions, is the number of subtrees of some tree.