Some basic observations on Kelly's conjecture for graphs
β Scribed by Bennet Manvel
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 457 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Kotzig (see Bondy and Murty (1976)) conjectured that there exists no graph with the property that every pair of vertices is connected by a unique path of length k, k>2. Here we prove this conjecture for k> 12.
Let 7(G) be the domination number of a graph G, and let G ΓH be the direct product of graphs G and H. It is shown that for any k t> 0 there exists a graph G such that 7(G Γ G) ~< 7(G) 2 -k. This in particular disproves a conjecture from .
## Abstract Let __G__ be a simple graph of order __n__ with Laplacian spectrum {Ξ»~__n__~, Ξ»~__n__β1~, β¦, Ξ»~1~} where 0=Ξ»~__n__~β€Ξ»~__n__β1~β€β β€Ξ»~1~. If there exists a graph whose Laplacian spectrum is __S__={0, 1, β¦, __n__β1}, then we say that __S__ is Laplacian realizable. In 6, Fallat et al. posed
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