Related papers: The Palindromic Trees
We generalize Schwenk's result that almost all trees contain any given limb to trees with positive integer vertex weights. The concept of characteristic polynomial is extended to such weighted trees and we prove that the proportion of…
We discuss some special property of the Farey sequence. We show in each term of the Farey sequence, ratio of the sum of elements in the denominator and the sum of elements in the numerator is exactly two. We also show that the Farey…
Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.
For an undirected tree with $n$ edges labelled by single letters, we consider its substrings, which are labels of the simple paths between pairs of nodes. We prove that there are $O(n^{1.5})$ different palindromic substrings. This solves an…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one can associate a tree in a natural way. It is known that the corresponding Poincare series P(X) = \sum_i N_i X^i is rational, where N_i is the number of nodes of the…
In this article we shows some results about algebra with the group of units having special polynomial identity.
We present a new characterization of $k$-trees based on their reduced clique graphs and $(k+1)$-line graphs, which are block graphs. We explore structural properties of these two classes, showing that the number of clique-trees of a…
In this paper, we find computational formulae for generalized characteristic polynomials of graph bundles. We show that the number of spanning trees in a graph is the partial derivative (at (0,1)) of the generalized characteristic…
Recently, Ehrenborg and Van Willenburg defined a class of bipartite graphs that correspond naturally to Ferrers diagrams, and proved several results about them. We give bijective proofs for the (already known) expressions for the number of…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
The theory of Hubbard trees provides an effective classification of non-linear post-critically finite polynomial maps from \C to itself. This note will extend this classification to the case of maps from a finite union of copies of \C to…
In the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special classes of polynomial maps which have,…
Let G be a family of n-vertex graphs of uniform degree 2 with the property that the union of any two member graphs has degree four. We determine the leading term in the asymptotics of the largest cardinality of such a family. Several…
We consider polynomial maps described by so-called "(multivariate) linearized polynomials". These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps…
Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…
We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is non-increasing with respect to an ordering of…