In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti, Cornuéjols and Vušković [3], and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky, Robertson, Seymour and Thomas [2]. Then we apply the Reducing Pseudopath Method [13] to characterize the su...

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...

Perfect ternary arrays are closely related to difference sets and group invariant weighing matrices. A previous paper by one of the authors demonstrated strong restrictions on difference sets with parameters (120, 35, 10). A perfect ternary array with energy 25 and order 60 – PTA(60,25) – would obey an equation analogous to the difference set equation for (120, 35, 10). A perfect ternary array ...

The sandpile group of a graph G is an abelian group whose order is the number of spanning trees of G. We find the decomposition of the sandpile group into cyclic subgroups when G is a regular tree with the leaves are collapsed to a single vertex. This result can be used to understand the behavior of the rotor-router model, a deterministic analogue of random walk studied first by physicists and ...