Related papers: Chemical trees minimizing energy and Hosoya index
Chemical graphs are simple undirected connected graphs, where vertices represent atoms in a molecule and edges represent chemical bonds. A degree-based topological index is a molecular descriptor used to study specific physicochemical…
The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…
We describe a simple efficient algorithm that allows one to construct Monte-Carlo realizations of merger histories of dark matter halos. The algorithm is motivated by the excursion set model (Bond et al. 1991) for the conditional and…
For a graph consider the pairs of disjoint matchings which union contains as many edges as possible, and define a parameter $\alpha$ which eqauls the cardinality of the largest matching in those pairs. Also, define $\betta$ to be the…
We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the…
Using a mapping of compact polymers on the Manhattan lattice to spanning trees, we calculate exactly the average number of bends at infinite temperature. We then find, in a high temperature approximation, the energy of the system as a…
The boxicity of a graph G, denoted as box(G) is defined as the minimum integer t such that G is an intersection graph of axis-parallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the…
We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for…
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have…
The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial…
Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…
Density Estimation Trees can play an important role in exploratory data analysis for multidimensional, multi-modal data models of large samples. I briefly discuss the algorithm, a self-optimization technique based on kernel density…
This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in $\mathcal{T}_n$ and…
The energy of a simple graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let $C_n$ denote the cycle of order $n$ and $P^{6,6}_n$ the graph obtained from joining two cycles…
Homogeneous matroids are characterized by the property that strength equals fractional arboricity, and arise in the study of base modulus [22]. For graphic matroids, Cunningham [9] provided efficient algorithms for calculating graph…
In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the…
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree $\Delta$ can be decomposed into at most $\lceil(\Delta+1)/2\rceil$ linear forests. We prove that $\Delta/2…
We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$…
Minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs. These limits can be taken with free or wired boundary conditions and are denoted FMSF (free minimal spanning forest) and WMSF…
In a study on the structure--dependency of the total $\pi$-electron energy from 1972, Trinajsti\'c and one of the present authors have shown that it depends on the sums $\sum_{v\in V}d(v)^2$ and $\sum_{v\in V}d(v)^3$, where $d(v)$ is the…