Related papers: Two distance-regular graphs
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…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n|A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given.…
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…
We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU - qUD = rI. We construct examples based upon: the Fibonacci poset, permutations, standard Young tableau, and plane binary…
A weakly distance-regular digraph is thick if its attached scheme is regular. In this paper, we show that each commutative thick weakly distance-regular digraph has a thick weakly distance-regular subdigraph such that the corresponding…
We consider a distance-regular graph $\Gamma=(X, \mathcal R)$ called the bilinear forms graph $H_q(D,N-D)$; we assume $N>2D\geq 6$ and $q \not=2$. We show that $\Gamma$ satisfies the following strengthened version of the balanced set…
We look at the question of which distance-regular graphs are core-complete, meaning they are isomorphic to their own core or have a complete core. We build on Roberson's homomorphism matrix approach by which method he proved the…
A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative…
We show that the categories of directed and undirected reflexive graphs carry exactly two (up to isomorphism) biclosed monoidal structures.
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while…
A graph is a cograph if it is $P_4$-free. A $k$-polar partition of a graph $G$ is a partition of the set of vertices of $G$ into parts $A$ and $B$ such that the subgraph induced by $A$ is a complete multipartite graph with at most $k$…
Fiol, Garriga, and Yebra introduced the notion of pseudo-distance-regular vertices, which they used to develop a new characterization of distance-regular graphs. Building on that work, Fiol and Garriga developed the spectral excess theorem…
A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and…
The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…
In this paper we consider how the following three objects are related: (i) the dual polar graphs; (ii) the quantum algebra U_q(sl_2); (iii) the Leonard systems of dual q-Krawtchouk type. For convenience we first describe how (ii) and (iii)…
We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance…
A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance…
Let the Kneser graph $K$ of a distance-regular graph $\Gamma$ be the graph on the same vertex set as $\Gamma$, where two vertices are adjacent when they have maximal distance in $\Gamma$. We study the situation where the Bose-Mesner algebra…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…