相关论文: Weakly distance-regular digraphs whose attached as…
A weak pseudoline arrangement is a topological generalization of a line arrangement, consisting of curves topologically equivalent to lines that cross each other at most once. We consider arrangements that are outerplanar---each crossing is…
In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three…
Weakly separated collections arise in the cluster algebra derived from the Pl\"ucker coordinates on the nonnegative Grassmannian. Oh, Postnikov, and Speyer studied weakly separated collections over a general Grassmann necklace $\mathcal{I}$…
A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many…
The dodecacode is a nonlinear additive quaternary code of length $12$. By puncturing it at any of the twelve coordinates, we obtain a uniformly packed code of distance $5$. In particular, this latter code is completely regular but not…
A mixed graph is a graph with undirected and directed edges. Guo and Mohar in 2017 determined all mixed graphs whose Hermitian spectral radii are less than $2$. In this paper, we give a sufficient condition which can make Hermitian spectral…
We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…
We present an approximation by conjugation scheme to obtain real-analytic diffeomorphisms of odd dimensional spheres that are weakly mixing with respect to the volume.
In this paper we will look at the relationship between the intersection number c2 and its diameter for a distance-regular graph. And also, we give some tools to show that a distance-regular graph with large c2 is bipartite, and a tool to…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
In this paper we show that certain almost distance-regular graphs, the so-called $h$-punctually walk-regular graphs, can be characterized through the cospectrality of their perturbed graphs. A graph $G$ with diameter $D$ is called…
Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we…
The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of weak…
We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…
A graph $G$ with $d+1$ distinct eigenvalues is called strongly distance-regular if $G$ itself is distance-regular, and its distance-$d$ graph $G_d$ is strongly-regular. In this note we provide a spectral characterization of those…
We study the structure of weakly-closed nonself-adjoint algebras arising from representations of single vertex 2-graphs. These are the algebras generated by 2 isometric tuples which satisfy a certain commutation relation. We show that these…
A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, J{\o}rgensen et al. \cite{JG14} initiated the study of doubly regular team…
Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of $3$-cycles at least 2 and no cycles of lengths $5, 6, 7$…
In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross-section of a three-dimensional system…
We extend Hoffman's coclique bound for regular digraphs with the property that its adjacency matrix is normal, and discuss cocliques attaining the inequality. As a consequence, we characterize skew-Bush-type Hadamard matrices in terms of…