Characterizing regular covers of edge-transitive or arc-transitive graphs is currently a hot topic in algebraic graph theory. In this paper, we will classify arctransitive regular cyclic covers of the complete bipartite graph Kp,p for each odd prime p. The classification consists of four infinite families of graphs. In particular, such covers exist for each odd prime p. The regular elementary a...

A graph is semi-symmetric if it is regular and edge transitive but not vertex transitive. The 3and 4-valent semi-symmetric graphs are wellstudied. Several papers describe infinite families of such graphs and their properties. 3-valent semi-symmetric graphs have been completely classified up to 768 vertices. The goal of this project is to extend this work to 5-valent semi-symmetric graphs. In th...

All node certificate based transitive signature schemes available in the literature make use of any digital signature scheme which is assumed to be provably secure against adaptive chosen-message attack, as a building block to produce node certificates in a graph. Consequently the algebraic structures to represent nodes in the graph are independent of the algebraic structure of signature scheme...

A fruitful way of studying groups is by means of their actions on graphs. A very special and interesting class of groups are the ones acting distance-transitively on some graph. A group G acting on a connected graph F = (VT, ET) is said to act distance-transitively if its action on each of the sets {(x, y)\ x, y e VT, d(x, y) = i} is transitive. Here VT and ET stand for the vertices and edges o...

It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs...

MOTIVATION Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular ...

All node certificate based transitive signature schemes available in the literature make use of any digital signature scheme which is assumed to be provably secure against adaptive chosen-message attack, as a building block to produce node certificates in a graph. Consequently the algebraic structures to represent nodes in the graph are independent of the algebraic structure of signature scheme...

In a recent paper (arXiv:1505.01475 ) Estélyi and Pisanski raised a question whether there exist vertex-transitive Haar graphs that are not Cayley graphs. In this note we construct an infinite family of trivalent Haar graphs that are vertex-transitive but non-Cayley. The smallest example has 40 vertices and is the well-known Kronecker cover over the dodecahedron graph G(10, 2), occurring as the...

In the paper we show that all combinatorial triangle-free configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (183) triangle-free configuration and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric realizations of the unique flag transitive triangle-free configuration (203) and the unique point tr...

A family of arc-transitive graphs is studied. The vertices of these graphs are ordered pairs of distinct points from a finite projective line, and adjacency is defined in terms of the cross ratio. A uniform description of the graphs is given, their automorphism groups are determined, the problem of isomorphism between graphs in the family is solved, some combinatorial properties are explored, a...