Counting Configurations in Designs

AbstractGiven a t-(v, k, λ) design, form all of the subsets of the set of blocks. Partition this collection of configurations according to isomorphism and consider the cardinalities of the resulting isomorphism classes. Generalizing previous results for regular graphs and Steiner triple systems, we give linear equations relating these cardinalities. For any fixed choice of t and k, the coefficients in these equations can be expressed as functions of v and λ and so depend only on the design's parameters, and not its structure. This provides a characterization of the elements of a generating set for m-line configurations of an arbitrary design

Review of: Graph Theory by J. A. Bondy and U. S. R. Murty

The article reviews the book Graph Theory, by J. A. Bondy and U. S. R. Murty

Review of: A Java Library of Graph Algorithms and Optimization by Hang T. Lau

The article reviews the book A Java Library of Graph Algorithms and Optimization, by Hang T. Lau

Review of: Assignment Problems by Rainer Burkard, Mauro Dell\u27Amico, and Silvano Martello

The article reviews the book Assignment Problems, by Rainer Burkard, Mauro Dell\u27Amico and Silvano Martello

Review of: Vector Calculus by Michael Corral

The article reviews the book Vector Calculus, by Michael Corral

Sage (version 3.4); The Princeton Companion To Mathematics

The article reviews the mathematics software Sage Version 3.4 from Sage Group

Review of: Pearls Of Discrete Mathematics by Martin Erickson

This article reviews the book Pearls of Discrete Mathematics, by Martin Erickson

Review of: Graph Theory by Reinhard Diestel

This article reviews the book Graph Theory, by Reinhard Diestel

The matching polynomial of a regular graph

AbstractThe matching polynomial of a graph has coefficients that give the number of matchings in the graph. For a regular graph, we show it is possible to recover the order, degree, girth and number of minimal cycles from the matching polynomial. If a graph is characterized by its matching polynomial, then it is called matching unique. Here we establish the matching uniqueness of many specific regular graphs; each of these graphs is either a cage, or a graph whose components are isomorphic to Moore graphs. Our main tool in establishing the matching uniqueness of these graphs is the ability to count certain subgraphs of a regular graph

Real-time monitoring of the heat of transfer of a homologous series of m-alkoxy phenols from isotonic aqueous solution to bacterial cells

Heats of dissolution of a homologous series of m-alkoxy phenols in an osmotically stable isotonic solution and in the same media containing a suspension of Escherichia coli cells were obtained by a differential heat conduction batch calorimeter at 298 K. The calorimetric curves show an initial rapid endothermic dissolution of the solute, followed by an exothermic process. From the heats of solution, the heat of transfer (Qtrs) of these compounds from the aqueous solution to the cells was calculated. The heat of transfer is exothermic and increases with the hydrophobicity of the compounds due to the biological consequences of the interaction process with the lipidic phase