Thea Kølsen Fischer, Cécile Viboud, Umesh Parashar, Mark Malek, Claudia Steiner, Roger Glass, and Lone Simonsen Division of Viral Diseases, National Center for Immunization and Respiratory Diseases, and Epidemiology Intelligence Service, Centers for Disease Control and Prevention, Atlanta; Department of Epidemiology Research, Statens Serum Institut, Copenhagen, Denmark; Fogarty International Ce...

In this paper, we consider Harary graphs as candidate solutions for the design of a physical network topology that achieves a high level of reliability using unreliable network elements. Our network model, which is motivated by the use of all-optical networks for high-reliability applications, is one in which nodes are invulnerable and links are subject to failure in a statistically independent...

Given a finite configuration of points in a metric space, a Steiner center (respectively, a centroid) is the point of the space (respectively, of the configuration) that minimizes the sum of the distances from all its elements. Working on the k-dimensional real space endowed with the Manhattan distance, we study the approximate algorithm that takes a point of minimum distance from the Steiner c...

The block intersection graph of a combinatorial design with block set B is the graph with B as its vertex set such that two vertices are adjacent if and only if their associated blocks are not disjoint. The chromatic index of a graph G is the least number of colours that enable each edge of G to be assigned a single colour such that adjacent edges never have the same colour. A graph G for which...

Professor Frank Harary has had a singular influence on graph theory through his own extensive original research, through the training of several researchers who themselves have made many important contributions, and through popularizing work, most significantly his text Graph Theory [1]. Frank Harary has contributed to a number of more advanced specialized texts, like that of Buckley and Harary...

We present new functional equations for the species of plane and of planar in the sense of Harary and Palmer, 1973 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e.a classiication of their structures according to their stabilizers. Therein result explicit formulas in terms of Catalan numbers for their associated generating series...

job satisfaction of employees is one of the most challenging concepts in any organization and is the basis for many of the policies and management strategies to increase productivity and efficiency. it is influenced by many factors including environmental and personal factors, income, nature and social status of the job, organizational prestige, promotion, job security, lack of role ambiguity, ...

Assuming that G is a finite group and H subgroup of G, the graph known as relative coprime with respect to (denoted Γ_(G,H)) has vertices corresponding elements G. Two distinct x y are adjacent by an edge if only (|x|,|y|)=1 or belongs H. This paper will focus on finding general formula for some topological indices dihedral group. The study in theory offers valuable insights into structural pro...

The Shields-Harary numbers are a class of graph parameters thatmeasure a certain kind of robustness of a graph, thought of as a network of fortified reservoirs, with reference to a given cost function. We prove a result about the Shields-Harary numbers with respect to concave continuous cost functions which will simplify the calculation of these numbers for certain classes of graphs, including ...

Frank Harary contributed numerous questions to a variety of topics in graph theory. One of his favourite topics was the Reconstruction Problem which, in its first issue in 1977, the Journal of Graph Theory described as the major unsolved problem in the field. Together with Plantholt, Frank Harary initiated the study of reconstruction numbers of graphs. We shall here present a survey of some of ...