Peter Rowlinson

Learn More
We prove that the minimum value of the least eigenvalue of the signless Laplacian of a connected nonbipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices. © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50
A graph is said to be exceptional if it is connected, has least eigenvalue greater than or equal to 2; and is not a generalized line graph. Such graphs are known to be representable in the exceptional root system E8: We determine the maximal exceptional graphs by a computer search using the star complement technique, and then show how they can be found by(More)
We consider only finite undirected graphs without loops or multiple edges. Let G be a non-trivial connected graph whose vertices are labelled 1,2,..., n and let A be the corresponding (0, l)-adjacency matrix of G. Let A have spectral form to Px + . . . + fim Pm where to > ... > //m: the largest eigenvalue nx is called the index of G. For ie ( 1 , . . . , m)(More)
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)
Let T be a tree of order n > 6 with μ as a positive eigenvalue of multiplicity k. Star complements are used to show that (i) if k > n/3 then μ = 1, (ii) if μ = 1 then, without restriction on k, T has k+ 1 pendant edges that form an induced matching. The results are used to identify the trees with a non-zero eigenvalue of maximum possible multiplicity.
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)