- Full text PDF available (33)
- This year (1)
- Last 5 years (12)
- Last 10 years (28)
Journals and Conferences
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
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.
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 discuss means of constructing fullerene graphs from their eigenvalues and angles. An algorithm for such a construction is given. © 2002 Elsevier Science Inc. All rights reserved.
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)