I describe a 27-vertex graph that is vertex-transitive and edgetransitive but not 1-transitive. Thus while all vertices and edges of this graph are similar, there are no edge-reversing automorphisms. A graph (undirected, without loops or multiple edges) is said to be vertextransitive if its automorphism group acts transitively on the set of vertices, edge-transitive if its automorphism group ac...

a graph $gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $gamma$ acts transitively on $v(gamma)$ or $e(gamma)$‎, ‎respectively‎. ‎let $gamma=cay(g,s)$ be a cayley graph on $g$ relative to $s$‎. ‎then, $gamma$ is said to be normal edge-transitive‎, ‎if $n_{aut(gamma)}(g)$ acts transitively on edges‎. ‎in this paper‎, ‎the eigenvalues of normal edge-tra...

In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and triacontahedron, only known polytopes (besides polygons) that are edge-transitive without being vertex-transitive. We show these polyhedra do not have higher-dimensional analogues, is, in dimension d ? 4, edge-transitivity of convex implies vertex-transitivity.More generally, we give a classific...

A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work...

In [5] we showed, that a doubly transitive, non-solvable dimensional dual hyperoval D is either isomorphic to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine the doubly transitive dimensional dual hyperovals, it remains to classify the doubly transitive, solvable dimensional dual hyperovals and this paper is a contribution to this problem. A dou...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...