Related papers: A note on 'A New Approach To Compute Wiener Index'
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and…
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded…
Graph theory provides powerful tools for modeling concepts in number theory, leading to the introduction of graphs derived from arithmetic properties. One such structure is the divisor prime graph, $G_{Dp(n)}$. For any positive integer $n$,…
Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from…
A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing a weight of a given citation, dependent on the previous scientific achievements of the author of the citing…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
Detection of boundaries of materials stored in transparent vessels is essential for identifying properties such as liquid level and phase boundaries, which are vital for controlling numerous processes in the industry and chemistry…
The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of R and two vertices are adjacent if their product is zero. The compressed zero divisor graph $\Gamma_E[R]$ is…
The eccentric sequence of a connected graph $G$ is the nondecreasing sequence of the eccentricities of its vertices. The Wiener index of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The unique trees that…
Tumor detection in biomedical imaging is a time-consuming process for medical professionals and is not without errors. Thus in recent decades, researchers have developed algorithmic techniques for image processing using a wide variety of…
We introduce a new graph invariant that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with…
We present a simple and faster algorithm for computing fair cuts on undirected graphs, a concept introduced in recent work of Li et al. (SODA 2023). Informally, for any parameter $\epsilon>0$, a $(1+\epsilon)$-fair $(s,t)$-cut is an…
We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the…
In this work authors significantly improved previous estimates of the number of edges in subgraphs of the special distance graph.
This manuscript presents a general recursive formula to estimate the size of fibers associated with algebraic maps from graphs to summary statistics of importance for social network analysis, such as number of edges (graph density), degree…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron--Martin), differential calculus (Malliavin), support description (Stroock--Varadhan),…
In this paper I prove good estimates on the moments and tail distribution of $k$-fold Wiener--It\^o integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the…
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…