‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

Denote the n × n toroidal queen’s graph by Qn. We find its automorphism group Aut(Qn) for each positive integer n, showing that for n ≥ 6, Aut(Qn) is generated by the translations, the group of the square, the homotheties, and (for odd n) the automorphism (x, y) → (y + x, y − x). For each n we find the automorphism classes of edges of Qn, in particular showing that for n > 1, Qn is edge-transit...

In early 2000’s, Rivest [1,2] and Micali [2] introduced the notion of transitive signature, which allows a third party with public key to generate a valid signature for a composed edge (vi,vk), from the signatures for two edges (vi,v j) and (v j,vk). Since then, a number of works, including [2,3,4,5,6], have been devoted on transitive signatures. Most of them address the undirected transitive s...

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive transitively set of -arcs. In this paper, we present a classification for those graphs that are have soluble edge-stabilizers.

A decomposition of a graph is a partition of the edge set, giving a set of subgraphs. A transitive decomposition is a decomposition which is highly symmetrical, in the sense that the subgraphs are preserved and transitively permuted by a group of automorphisms of the graph. This paper describes some ‘product’ constructions for transitive decompositions of graphs, and shows how these may be used...

A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. In this paper we give some background to the study of transitive decompositions and highlight a connection with partial linear spaces. We then describe a simple method for constructing transitive decompositi...

A graph is said to be half-arc-transitive if its automorphism group acts transitively on the set of its vertices and edges but not on the set of its arcs. With each half-arc-transitive graph of valency 4 a collection of the so called alternating cycles is associated, all of which have the same even length. Half of this length is called the radius of the graph in question. Moreover, any two adja...

Tian and Meng in [Y. Tian and J. Meng, c  -Optimally half vertex transitive graphs with regularity , Information Processing Letters 109 (2009) 683-686] shown that a connected half vertex transitive graph with regularity and girth is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree k k   6 g G   ...

Building on earlier results for regular maps and orientably chiral maps, we classify the non-abelian finite simple groups arising as automorphism of in each 14 Graver–Watkins classes edge-transitive maps.