Related papers: A relation on trees and the topological indices ba…
This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes…
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics…
The {\em atom-bond connectivity (ABC) index} is a degree-based graph topological index that found chemical applications. The problem of complete characterization of trees with minimal $ABC$ index is still an open problem.…
The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's…
The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and is…
We investigate how the topology of attributed graphs influences the distribution of node attributes. This work offers a novel perspective by treating topology and attributes as structurally distinct but interacting components. We introduce…
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applications in data analysis and scientific visualization. In this…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…
In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy \[…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree…
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…
This paper presents our studies on the rearrangement of links from the structure of websites for the purpose of improving the valuation of a page or group of pages as established by a ranking function as Google's PageRank. We build our…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
Vertex-degree-based topological indices have recently gained a lot of attention from mathematical chemists. One such index that we focus on in this paper is called Sombor index. After its definition in late 2020, the Sombor index was…
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
Recently, D. Vuki$\check{c}$evi$\acute{c}$ and J. Sedlar in \cite{Vuki} introduced an order "$\preceq$" on $\mathcal{T}_n$, the set of trees on $n$ vertices, such that the topological index $F$ of a graph is a function defined on the order…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…