Related papers: A note on extremal results on directed acyclic gra…
Recent investigations in computational biology have focused on a family of 2-colored digraphs, called 2-colored best match graphs, which naturally arise from rooted phylogenetic trees. Actually the defining properties of such graphs are…
A directed acyclic graph G = (V, E) is pseudo-transitive with respect to a given subset of edges E1, if for any edge ab in E1 and any edge bc in E, we have ac in E. We give algorithms for computing longest chains and demonstrate geometric…
We associate each endomorphism of a finite cyclic group with a digraph and study many properties of this digraph, including its adjacent matrix and automorphism group.
An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich…
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
We present a method to generate directed acyclic graphs (DAGs) using deep reinforcement learning, specifically deep Q-learning. Generating graphs with specified structures is an important and challenging task in various application fields,…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
Given a pair of distinct vertices u, v in a graph G, we say that s is a junction of u, v if there are in G internally vertex disjoint directed paths from s to u and from s to v. We show how to characterize junctions in directed acyclic…
This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…
We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs for the actions of these groups on $d-$regular rooted trees…
An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented…
We present lower and upper bounds for the geometric-arithmetic index of unicyclic graphs and provide extremal graphs for the corresponding bounds.
A general expression for calculating the bond incident degree (BID) indices of certain triangular chain graphs is derived. The extremal triangular chain graphs with respect to several well known BID indices are also characterized over a…
It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilisers. However, beside a well known family of exceptional graphs, related to the lexicographic product of a cycle…
In applications, quantities of interest are often modelled in equilibrium or an equilibrium solution is sought. The presence of confounding makes causal inference in this setting challenging. We provide interpretable graphical models for…
Extremal Graph Theory aims to determine bounds for graph invariants as well as the graphs attaining those bounds. We are currently developping PHOEG, an ecosystem of tools designed to help researchers in Extremal Graph Theory. It uses a big…
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…