Related papers: The Separated Box Product of Two Digraphs
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…
We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The…
We use the lens of Zappa--Sz\'ep decomposition to examine the relationship between directed graph products and $k$-graph products. There are many examples of higher-rank graphs, or $k$-graphs, whose underlying directed graph may be factored…
Structural balance theory assumes triads in networks to gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for considering…
We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously.…
We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the structure of finite and infinite directed graphs with respect…
A new class of simple symmetric digraphs called $\mathcal{D}$ is defined and studied here. Any digraph in $\mathcal{D}$ has the property that each non-pendant vertex is adjacent to at least one pendant vertex. A graph theoretical…
In this paper the analogy between differential forms arising from integrals in additive calculus and forms arising from the integrals in product calculus is investigated. It is found that with an appropriate definition of scalar…
In this note we consider $k$-regular multigraphs, where the possible edge multiplicities are controlled. These structures are considered in a question recently posed by Brendan McKay. We express the generating functions using the scalar…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
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…
We classify all Hopf algebras which factorize through two Taft algebras $\mathbb{T}_{n^{2}}(\bar{q})$ and respectively $T_{m^{2}}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\bar{q} \neq…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…
We study coherence of graph products and Coxeter groups and obtain many results in this direction.
We prove that if $X$ is a paracompact connected space and $Z=\prod_{s\in S}Z_s$ is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map $g:X\to Z$ there exists a separately…
This article investigates the properties of order-divisor graphs associated with finite groups. An order-divisor graph of a finite group is an undirected graph in which the set of vertices includes all elements of the group, and two…
This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.
A $k$-regular graph on $v$ vertices is a {\em divisible design graph} if there exist integers $\lambda_1,\lambda_2,m,n$ such that the vertex set can be partitioned into $m$ classes of size $n$ and any two different vertices from the same…