This paper provides an overview of research developments toward nanometer-scale electronic switching devices for use in building ultra-densely integrated electronic computers. Specifically, two classes of alternatives to the field-effect transistor are considered: 1) quantum-effect and single-electron solid-state devices and 2) molecular electronic devices. A taxonomy of devices in each class is provided, operational principles are described and compared for the various types of devices, and the literature about each is surveyed. This information is presented in nonmathematical terms intended for a general, technically interested readership

In 1996, Reed proved that the domination number γ(G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that γ(H)�⌈n/3 ⌉ for every connected 3-regular (cubic) n-vertex graph H. In this note, we disprove this conjecture. We construct a connected cubic graph G on 60 vertices with γ(G) = 21 and present a sequence {Gk} ∞ k=1 of connected cubic graphs with lim k→∞ γ(Gk) 8 1 1

Abstract. In 1996, Reed proved that the domination number, γ(G), of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper, improving an upper bound by Kostochka and Stodolsky we show that for n> 8 the domination number of every n-vertex cubic connected graph is at most ⌊5n/14⌋. This bound is sharp for even 8 < n ≤ 18.