Related papers: Some Euler-type formulas for planar graphs

Creating comprehensible visualizations of highly overlapping set-typed data is a challenging task due to its complexity. To facilitate insights into set connectivity and to leverage semantic relations between intersections, we propose a…

In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…

Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…

We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of…

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs…

Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems…

In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used…

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…

In this paper, we find a new recurrence formula fo the Euler zeta functions.

Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…

These are some informal remarks on quadratic orbital networks over finite fields. We discuss connectivity, Euler characteristic, number of cliques, planarity, diameter and inductive dimension. We find a non-trivial disconnected graph for…

We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…

We propose a graph-oriented attention-based explainability method for tabular data. Tasks involving tabular data have been solved mostly using traditional tree-based machine learning models which have the challenges of feature selection and…

Some notes and observations on analytic functions defined on an annulus