for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Background Chlamydia trachomatis is considered as an important cause of preventable sexually transmitted diseases worldwide. It is known to be of an obligate intracellular nature and enters its target cells via an endocytic process. As major outer membrane protein (MOMP) is one of the main candidates for the attachment and entry of chlamydia to the host cells we have tried to label the epitopes...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

Graph-theoretic structures are an obvious means to reason about systems of asynchronous processes. Their dynamic behaviour can be simulated by applying productions of a graph grammar. The present paper is motivated by looking for a formal method that is able to describe the behaviour of systems of processes that share data structures. We generalize the categorical graph-grammar approach by labe...

Let G = (V; E) denote a nite simple undirected connected graph of order n = jV j and diameter D. For any integer k 2 1; D], a proper k-colouring of G is a labelling of the vertices V such that no two distinct vertices at distance k or less have the same label. We let k (G), the k-chromatic number of G, denote the least number of labels required to achieve a proper k-colouring of G. In this pape...

Motivated by problems in radio channel assignment, we consider the vertexlabelling of graphs with nonnegative integers. The objective is to minimize the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with the associa...

We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.

We provide binary labellings for the angles of quadrangulations and plane Laman graphs which are in analogy with Schnyder labellings for triangulations [W. Schnyder, Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990].