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We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results are presented in the context of a number of computer-generated conjectures.
p. cm. – (Encyclopedia of mathematics and its applications) Includes bibliographical references and index.
The milk and body temperatures of 15 cows were monitored twice daily at milking times, over a total of 30 oestrous periods. The best determination of oestrus was based on a temperature rise of at least 0.2 degree C over the corresponding mean temperature of the three preceding days. This resulted in 72 +/- 16 per cent of oestruses, predicted by serial… (More)
A general formula is obtained for the characteristic polynomial of a graph modied by the addition of a vertex with any prescribed set of neighbours.
Suppose that the positive integer μ is the eigenvalue of largest multiplicity in an extremal strongly regular graph G. By interlacing, the independence number of G is at most 4μ 2 + 4μ − 2. Star complements are used to show that if this bound is attained then either (a) μ = 1 and G is the Schläfli graph or (b) μ = 2 and G is the McLaughlin graph.
Four, rumen fistulated crossbred (Brahman × native) beef cattle steers were randomly assigned to receive four dietary treatments according to a 2 × 2 factorial arrangement in a 4 × 4 Latin square design. Factor A was carbohydrate source; cassava chip (CC) or CC + rice bran at a ratio 3:1 (CR3:1) and Factor B was cotton seed meal level (CM); and 109 g CP/kg… (More)
Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds québécois de la recherche sur la nature et les technologies. Abstract We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a… (More)