94 research outputs found
Regular graphs with maximal energy per vertex
We study the energy per vertex in regular graphs. For every k, we give an
upper bound for the energy per vertex of a k-regular graph, and show that a
graph attains the upper bound if and only if it is the disjoint union of
incidence graphs of projective planes of order k-1 or, in case k=2, the
disjoint union of triangles and hexagons. For every k, we also construct
k-regular subgraphs of incidence graphs of projective planes for which the
energy per vertex is close to the upper bound. In this way, we show that this
upper bound is asymptotically tight
Formal Properties of XML Grammars and Languages
XML documents are described by a document type definition (DTD). An
XML-grammar is a formal grammar that captures the syntactic features of a DTD.
We investigate properties of this family of grammars. We show that every
XML-language basically has a unique XML-grammar. We give two characterizations
of languages generated by XML-grammars, one is set-theoretic, the other is by a
kind of saturation property. We investigate decidability problems and prove
that some properties that are undecidable for general context-free languages
become decidable for XML-languages. We also characterize those XML-grammars
that generate regular XML-languages.Comment: 24 page
A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
The study of good nonregular fractional factorial designs has received
significant attention over the last two decades. Recent research indicates that
designs constructed from quaternary codes (QC) are very promising in this
regard. The present paper shows how a trigonometric approach can facilitate a
systematic understanding of such QC designs and lead to new theoretical results
covering hitherto unexplored situations. We focus attention on one-eighth and
one-sixteenth fractions of two-level factorials and show that optimal QC
designs often have larger generalized resolution and projectivity than
comparable regular designs. Moreover, some of these designs are found to have
maximum projectivity among all designs.Comment: Published in at http://dx.doi.org/10.1214/10-AOS815 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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