Moore Reports

Underhill Moore

Very few Moore Graphs

We prove here a well known result in graph theory, originally proved by Hoffman and Singleton, that any non-trivial Moore graph of diameter 2 is regular of degree k = 2, 3, 7 or 57. The existence (and uniqueness) of these graphs is known for k = 2, 3, 7 while it is still an open problem if there is a moore graph of degree 57 or not.

Multipartite Moore Digraphs

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, assuming that every vertex of a given partite set is adjacent to the same number of vertices (δ) in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distanceregular. Within this framework, some necessary conditions for the existence of a Moore r-parti...

Justin Tatch Moore

This note gives a “Zorn’s Lemma” style proof that any two bases in a vector space have the same cardinality. One of the most fundamental notions in linear algebra is that of a basis: A subset B of a vector space V is a basis if every element of V is a unique linear combination of elements of B. The following theorem of Georg Hamel expresses one of the most important aspects of this definition. ...

On Boyer-Moore Preprocessing

Probably the two best-known exact string matching algorithms are the linear-time algorithm of Knuth, Morris and Pratt (KMP), and the fast on average algorithm of Boyer and Moore (BM). The efficiency of these algorithms is based on using a suitable failure function. When a mismatch occurs in the currently inspected text position, the purpose of a failure function is to tell how many positions th...