Related papers: Neighbour-transitive codes in Kneser graphs

Let $\mathcal{D}$ be a set of straight-line segments in the plane, potentially crossing, and let $c$ be a positive integer. We denote by $P$ the union of the endpoints of the straight-line segments of $\mathcal{D}$ and of the intersection…

A finite simple graph $\Gamma$ is called a Nest graph if it is regular of valency $6$ and admits an automorphism $\rho$ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say…

Let $S$ be a set of transpositions generating the symmetric group $S_n$. The transposition graph of $S$ is defined to be the graph with vertex set $\{1,\ldots,n\}$, and with vertices $i$ and $j$ being adjacent in $T(S)$ whenever $(i,j) \in…

A graph $\Ga$ is $G$-symmetric if $\Ga$ admits $G$ as a group of automorphisms acting transitively on the set of vertices and the set of arcs of $\Ga$, where an arc is an ordered pair of adjacent vertices. In the case when $G$ is…

The Kneser graph $K(n,k)$ is defined for integers $n$ and $k$ with $n \geq 2k$ as the graph whose vertices are all the $k$-subsets of $[n]=\{1,2,\ldots,n\}$ where two such sets are adjacent if they are disjoint. The Schrijver graph $S(n,k)$…

Seymour Second Neighborhood Conjecture (SSNC) asserts that every finite oriented graph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood. Such a vertex is called a Seymour vertex. A digraph $D =…

The Kneser graph $K(n,k)$ is defined for integers $n$ and $k$ with $n \geq 2k$ as the graph whose vertices are all the $k$-subsets of $\{1,2,\ldots,n\}$ where two such sets are adjacent if they are disjoint. A classical result of Lov\'asz…

This paper initiates the investigation of the family of $(G,s)$-geodesic-transitive digraphs with $s\geq 2$. We first give a global analysis by providing a reduction result. Let $\Gamma$ be such a digraph and let $N$ be a normal subgroup of…

For integers $k\geq 1$ and $n\geq 2k+1$ the Kneser graph $K(n,k)$ has as vertices all $k$-element subsets of $[n]:=\{1,2,\ldots,n\}$ and an edge between any two vertices (=sets) that are disjoint. The bipartite Kneser graph $H(n,k)$ has as…

A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. If $W$ is $k$-uniform (each letter of $W$ occurs exactly $k$…

For $k,s\geq2$, the $s$-stable Kneser graphs are the graphs with vertex set the $k$-subsets $S$ of $\{1,\ldots,n\}$ such that the circular distance between any two elements in $S$ is at least $s$ and two vertices are adjacent if and only if…

A cycle-transversal of a graph G is a subset T of V(G) such that T intersects every cycle of G. A clique cycle-transversal, or cct for short, is a cycle-transversal which is a clique. Recognizing graphs which admit a cct can be done in…

We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…

Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…

Using dominating sets to separate vertices of graphs is a well-studied problem in the larger domain of identification problems. In such problems, the objective is to choose a suitable dominating set $C$ of a graph $G$ which is also…

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called…

A directed graph $G=(V,E)$ is {\it strongly pseudo transitive} if there is a partition $\{A,E-A\}$ of $E$ so that graphs $G_1=(V,A)$ and $G_2=(V,E-A)$ are transitive, and additionally, if $ab\in A$ and $bc\in E $ implies that $ac\in E$. A…

We study the minimal crossing number $c(K_{1}\# K_{2})$ of composite knots $K_{1}\# K_{2}$, where $K_1$ and $K_2$ are prime, by relating it to the minimal crossing number of spatial graphs, in particular the $2n$-theta curve…

We study transitivity properties of graphs with more than one end. We completely classify the distance-transitive such graphs and, for all $k \geq 3$, the $k$-CS-transitive such graphs.

A graph $\Gamma$ is called edge-regular whenever it is regular and for any two adjacent vertices, the number of their common neighbors is independent of the choice of vertices. A clique $C$ in $\Gamma$ is called regular whenever for any…