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Changing and unchanging of the radius of a graph

✍ Scribed by Ronald D. Dutton; Sirisha R. Medidi; Robert C. Brigham

Book ID
107826665
Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
991 KB
Volume
217
Category
Article
ISSN
0024-3795

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πŸ“œ SIMILAR VOLUMES

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Every graph can be represented as the intersection graph on a family of closed unit cubes in Euclidean space E". Cube vertices have integer coordinates. The coordinate matrix, A(G) = {v.~} of a graph G is defined by the set of cube coordinates. The imbedded dimension of a graph, BP(G), is a number

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We provide upper estimates on the spectral radius of a directed graph. In particular w e prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.

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On the hamiltonian index and the radius
On the hamiltonian index and the radius of a graph
✍ Marko LovrečičSaraαΊ‘in πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 316 KB

Catlin et al. [1, Corollary 9A] characterised the graphs G with the property that ham(G) > rad(G) + 1 where ham(G) and rad(G) stand for the hamiltonian index and the radius of G, respectively. Here a slightly stronger result is presented. In effect, the graphs for which ham(G) > rad(G) holds are ch