Partitions in Matrices and Graphs
โ Scribed by Hughes, D.R.; Singhi, N.M.
- Book ID
- 123536343
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 831 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let G be a graph with adjacency matrix A, and let I-be the set of all permutation matrices which commute with A. We call G compact if every doubly stochastic matrix which commutes with A is a convex combination of matrices from I'. We characterize the graphs for which S( A) = {I} and show that the a
Let G be a graph and n โฅ 2 an integer. We prove that the following are equivalent: (i) there is a partition , and (ii) for every subset S of V (G), G \ S has at most n|S| components with the property that each of their blocks is an odd order complete graph.