Related papers: A relation on trees and the topological indices ba…
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting…
In this paper we disprove three conjectures from [M. Dehmer, F. Emmert-Streib, Y. Shi, Interrelations of graph distance measures based on topological indices, PLoS ONE 9 (2014) e94985] on graph distance measures based on topological indices…
This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs.…
Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indexes, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial…
The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum…
The Horton-Strahler (HS) index $r=\max{(i,j)}+\delta_{i,j}$ has been shown to be relevant to a number of physical (such at diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
A tree T is invertible if and only if T has a perfect matching. Godsil considers an invertible tree T and finds that the inverse of the adjacency matrix of T has entries in {0, 1, -1} and is the signed adjacency matrix of a graph which…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Interaction networks are of central importance in post-genomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main…
The number of topologically different plane real algebraic curves of a given degree $d$ has the form $\exp(C d^2 + o(d^2))$. We determine the best available upper bound for the constant $C$. This bound follows from Arnold inequalities on…