Small non-Leighton two-complexes

Small graphs with exactly two non-negative eigenvalues

Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

Chris Leighton

Electronic and magnetic materials are the central focus of our group's research. We study a wide variety of types of materials such as nanostructures, thin films, multilayered heterostructures, and bulk polycrystals and single crystals. We have interests in several areas including the interplay between electronic transport and magnetism in novel materials, and the study of interfaces between di...

Amending Leighton and Micali's Key Distribution Protocol

A key distribution protocol is a set of rules by which two users can establish a shared common key between them and then use the key in future secure communications. We analyze a key distribution protocol presented by Leighton and Micali at the CRYPTO'93 conference, which is based on tamper-proof hardware, and show that the protocol fails in that a common key shared between two users can always...

Ca 2 + waves in the heart Leighton

Tom Leighton and Eric Lehman Problem Set 3 Solutions