the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

An infinite countable Steiner triple system is called universal if any countable Steiner triple system can be embedded into it. The main result of this paper is the proof of non-existence of a universal Steiner triple system. The fact is proven by constructing a family S of size 2 of infinite countable Steiner triple systems so that no finite Steiner triple system can be embedded into any of th...

We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (St...

The diameter of a graph is an important factor for communication as it determines the maximum communication delay between any pair of processors in a network. Graham and Harary [N. Graham, F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Applied Mathematics 37/38 (1992) 265–274] studied how the diameter of hypercubes can be affected by increasing and decreasing edges. Th...

For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W -tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steine...

Use of HL-60 Cell Line To Measure Opsonic Capacity of Pneumococcal Antibodies R. A. Fleck,* S. Romero-Steiner, and M. H. Nahm National Institute for Biological Standards and Control, South Mimms, Potters Bar, Hertfordshire, United Kingdom; Division of Bacterial and Mycotic Diseases, National Center for Infectious Diseases, Centers for Disease Control and Prevention, Atlanta, Georgia; and Depart...

John Grienenberger, Ph.D. is a recent graduate of the doctoral program in clinical psychology at the City University of New York. He is currently Child Program Coordinator at the Wright Institute Los Angeles and in private practice as a psychological assistant in West Los Angeles. Dr. Grienenberger would like to thank Gary Cox-Steiner, Ph.D. and the Center for Mental Health Promotion for the ge...

Steiner systems are a fascinating topic of combinatorics. The most studied Steiner systems are S(2,3,v) (Steiner triple systems), S(3,4,v) (Steiner quadruple systems), and S(2,4,v). There are a few infinite families of Steiner systems S(2,4,v) in the literature. The objective of this paper is to present an infinite family of Steiner systems S(2,4,2m) for all m ≡ 2 (mod 4)≥ 6 from cyclic codes. ...

Given an edge-weighted graph G = (V,E) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R. A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we present a 20-approximation algorithm for the full Steiner tree problem when G is a...