In this note we use eigenvalues of folded cubes to simplify an analogue of Kelly's Lemma for vertex-switching reconstruction due to Krasikov and Roditty. Our new version states that the number of subgraphs (or induced subgraphs) of an n-vertex graph G isomorphic to a given m-vertex graph can be foun
Switching reconstruction of digraphs
β Scribed by J. A. Bondy; F. Mercier
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 186 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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## Abstract A graph is called __sβvertex switching reconstructible__ (__s__βVSR) if it is uniquely defined, up to isomorphism, by the multiset of unlabeled graphs obtained by switching of all its __s__βvertex subsets. We show that a graph with __n__ vertices is __n__/2βVSR if __n__ = 0(mod 4), (__n
## Abstract A hypotraceable digraph is a digraph __D__ = (__V, E__) which is not traceable, i.e., does not contain a (directed)Hamiltonian path, but for which __D__ β __v__ is traceable for all __ve__ β __V__. We prove that a hypotraceable digraph of order __n__ exists iff __n__ β₯ 7 and that for ea
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