Factorization Index for Completely Positive Graphs
β Scribed by Xiao Dong Zhang; Jiong Sheng Li
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2002
- Tongue
- English
- Weight
- 183 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1439-7617
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π SIMILAR VOLUMES
We complete the proof that a graph G is completely positive (every doubly nonnegative matrix A, with G(A) = G, is completely positive) if and only if it has no odd cycle of length greater than 4. i#j, aij#O}. Definition 1.3. A graph G is completely positizje if every doubly nonnegative matrix A with
In this paper we establish two results concerning completely positive graphs and their complements: (1) the complement of a completely positive graph on n 9 vertices is not completely positive; (2) the spectral radius of the adjacency matrix of a completely positive graph on n 6 vertices is at most
## Abstract A cube factorization of the complete graph on __n__ vertices, __K~n~__, is a 3βfactorization of __K~n~__ in which the components of each factor are cubes. We show that there exists a cube factorization of __K~n~__ if and only if __n__ β‘ 16 (mod 24), thus providing a new family of unifor