## Abstract We prove that if __K__ is an undirected, simple, connected graph of even order which is of class one, regular of degree __p__ โฅ 2 and such that the subgraph induced by any three vertices is either connected or null, then any graph __G__ obtained from __K__ by splitting any vertex is __p
Separation index of a graph
โ Scribed by Andrew Vince
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 89 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0364-9024
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โฆ Synopsis
Abstract
The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. ยฉ 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53โ61, 2002
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