Geometric aspects of 2-walk-regular graphs
✍ Scribed by Cámara, Marc; van Dam, Edwin R.; Koolen, Jack H.; Park, Jongyook
- Book ID
- 123174221
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 366 KB
- Volume
- 439
- Category
- Article
- ISSN
- 0024-3795
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## Abstract A graph is walk‐regular if the number of closed walks of length ℓ rooted at a given vertex is a constant through all the vertices for all ℓ. For a walk‐regular graph __G__ with __d__+1 different eigenvalues and spectrally maximum diameter __D__=__d__, we study the geometry of its __d__‐
Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Zhu and Li showed that the upper bound 3k on n can be relaxed to q k if G is 3-connected and k 2 63. We improve both results by showing that G is hamiltonian if n 5 gk -7 and G does not belong to a res