Related papers: Compositions of Digraphs: A Survey

In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.

A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the…

Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \in A(D)$. Clearly, a 2-quasi-transitive…

Additional remarks and questions for transseries. In particular: properties of composition for transseries; the recursive nature of the construction of R[[[ x ]]]; modes of convergence for transseries. There are, at this stage, questions…

We present an informal survey (meant to accompany another paper) on graph compression methods. We focus on lossless methods, briefly list available pproaches, and compare them where possible or give some indicators on their compression…

We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…

In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…

This paper is to accompany the Census of Edge-Transitive Tetravalent Graphs, available at jan.ucc.nau.edu/~swilson/C4FullSite/index.html, which is a collection of all known edge-transitive graphs of valence 4 up to 512 vertices. The Census…

We say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real. The essential cyclicity implies the presence of directed cycles, but not vice versa. The problem of characterizing essential cyclicity in terms of…

The families of graphs defined by a certain type of system of equations over commutative rings have been studied and used since 1990s. This survey presents these families and their applications related to graphs, digraphs, and hypergraphs.…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

Let $k$ be an integer with $k\geq 2$. A digraph $D$ is $k$-quasi-transitive, if for any path $x_0x_1\ldots x_k$ of length $k$, $x_0$ and $x_k$ are adjacent. Suppose that there exists a path of length at least $k+2$ in $D$. Let $P$ be a…

A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. In this paper we give some background to the study…

We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…

The presented work focuses on problems from determinant theory, set theory and topology. The term graph is the binding element that connects these problems. Graphs are distinguished by their geometrical simplicity, which helps in showing…

Despite a multitude of empirical studies, little consensus exists on whether neural networks are able to generalise compositionally, a controversy that, in part, stems from a lack of agreement about what it means for a neural model to be…

We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…

The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…