In this note a short new proof of Diestel's characterization theorem for infinite k-connected rayless graphs is given, using the concept of the order of a rayless graph which was introduced by R. Schmidt. 1998 Academic Press Diestel [3, Theorem 4.3] gives a beautiful description of the structure of
✦ LIBER ✦
A Note onk-walks in Bridgeless Graphs
✍ Scribed by Tomáš Kaiser; Roman Kužel; Hao Li; Guanghui Wang
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 201 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
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The aim of this note is to call attention to a simple regularity regarding the number of walks in a finite graph G. Let wk denote the number of walks of length k(> 0) in G. Then Wi+,, 5 W&Wzb holds for all a, b E NJ while equality holds exclusively either (I) for all a, b E No (in case G is a regula