Related papers: New Partial Geometric Difference Sets and Partial …
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…
Chen and Cheng [Ann. Statist. 34 (2006) 546--558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for $9N/32\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
G-structures and Cartan geometries are two major approaches to the description of geometric structures (in the sense of differential geometry) on manifolds of some fixed dimension $n$. We show that both descriptions naturally extend to the…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets; taking the set to be the vertex…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…
Classical Hamming graphs are Cartesian products of complete graphs, and two vertices are adjacent if they differ in exactly one coordinate. Motivated by connections to unitary Cayley graphs, we consider a generalization where two vertices…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
Various partially ordered Grothendieck group invariants are introduced for general operator algebras and these are used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric spaces generated by graphs and their shortest path metric…
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
In [S. Arumugam, V. Mathew and J. Shen, On fractional metric dimension of graphs, preprint], Arumugam et al. studied the fractional metric dimension of the cartesian product of two graphs, and proposed four open problems. In this paper, we…
The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppstein [Separating thickness from geometric thickness. In: Towards a…
The separation dimension of a graph $G$, written $\pi(G)$, is the minimum number of linear orderings of $V(G)$ such that every two nonincident edges are "separated" in some ordering, meaning that both endpoints of one edge appear before…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…