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.

Consider a connected undirected graph G = (V ,E), a subset of vertices C ⊆ V , and an integer r 1; for any vertex v ∈ V , let Br(v) denote the ball of radius r centred at v, i.e., the set of all vertices linked to v by a path of at most r edges. If for all vertices v ∈ V (respectively, v ∈ V \C), the setsBr(v)∩C are all nonempty and different, then we call C an r-identifying code (respectively,...

A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A locating-total dominating set of G is a total dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of...

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...

We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations, isolating unique states, duplication counting, or finding equivalence classes under identifiability constraints. A motivating application is locating equivalence ...

Self-stabilizing algorithms model distributed systems, which automatically recover from transient failures in the state of the system. The center of a graph comprises a set of vertices with minimum eccentricity. Farley and Proskurowski showed the linear time algorithm for locating the center of an outerplanar graph in the classical computing paradigm. The present paper investigates the selfstab...

We propose to determine fundamental circuits of two matroids induced by certain bipartite graphs derived from the network equations in order to detect and locate inconsistencies in large electrical networks. Our method is easy to implement, is very fast, and does not rely on a specific form of network equations. It has been implemented in an industrial circuit simulator and, despite its simplic...

This paper presents an approach to the specification of visual language syntax. Based on attributed graphs as the notion of abstract syntax, syntactical correctness is specified by a set of predicates over that structure. The proposed technique facilitates natural embedding of other visual and textual notations, the definition of complex syntactical and static-semantical properties, as well as ...

By exploiting the “correlation of deflections” phenomena, we propose a new bridge diagnosis method. First, we introduce the notion of deflection correlation DC graphs and propose a method for building a DC graph. Second, we present a new algorithm for locating the abnormal cliques. Finally, we demonstrate the potential utility of the new method by applying it to the simulated diagnosis of a rea...