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.

In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...

In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...

Whereas Moore’s law continues to push the industry to ever more complex technologies (More Moore) supporting sophisticated digital applications, the so-called More than Moore technologies are finding more and more heterogeneous application domains. EDA challenges in More Moore are related to power optimisation, DfM and verification needs whereas the More than Moore technologies require EDA tool...

ontemporary ethical theory begins with G. E. Moore (1873–1958). Moore opened up new issues for consideration and altered the focus of ethical discussion. Much of twentieth-century analytic ethics, at least until recently, treated issues that were raised by Moore or by philosophers responding either to him or to other respondents. Although analytic ethical philosophers discussed many questions t...

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...

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. ...

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...