On the Spectrum of the Derangement Graph

We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue

The distance spectra of Cayley graphs of Coxeter groups

The absolute (respectively, weak) order graph on a Coxeter group is the graph underlying the absolute (respectively, weak) order poset. We investigate the distance spectra of many of these graphs and pose several open problems

Manifolds, tensors and, forms: an introduction for mathematicians and physicists

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree theory. It also features over 250 detailed exercises, and a variety of applications revealing fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. Solutions to the problems are available for instructors at www.cambridge.org/9781107042193

On the Chromatic Number of the Complement of a Class of Line Graphs

Let G beagraph, G its complement, L(G) its line graph, and χ(G) its chromatic number. Then we have the following Theorem Let G be agraph with n vertices. (i) If G is triangle free, then n − 4 ≤ χ L(G) ≤ n − 2 (ii) If G is planar and every triangle bounds a disk, then n − 3 ≤ χ L(G) ≤ n −

Efficacy of endoscopic closure of acute perforations of the gastrointestinal tract

Acute perforations of the gastrointestinal tract are rare, severe complications of endoscopy that usually require surgical repair. Endoscopic repair of perforations would reduce the need for surgeries; we evaluated the efficacy and safety of endoscopic closure of acute perforations of the gastrointestinal tract by using a new clip device