In this paper, some sufficient conditions are given on a graph G, under which it is proved that G {x} is determined by the generalized spectrum iff G is determined by the generalized spectrum, where G {x} is the graph obtained from the graph G by adding an isolated vertex x.
On the spectral characterization of the union of complete multipartite graph and some isolated vertices
β Scribed by Haicheng Ma; Haizhen Ren
- Book ID
- 108114267
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 204 KB
- Volume
- 310
- Category
- Article
- ISSN
- 0012-365X
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In this paper we use Tutte's f-factor theorem and the method of amalgamations to find necessary and sufficient conditions for the existence of a k-factor in the complete multipartite graph K(p(1 ) ..... p(n)), conditions that are reminiscent of the Erd6s-Gallai conditions for the existence of simple
## Abstract It is known that a necessary condition for the existence of a 1βrotational 2βfactorization of the complete graph __K__~2__n__+1~ under the action of a group __G__ of order 2__n__ is that the involutions of __G__ are pairwise conjugate. Is this condition also sufficient? The complete ans