On minimum rank and zero forcing sets of a graph
β Scribed by Liang-Hao Huang; Gerard J. Chang; Hong-Gwa Yeh
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 217 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
For a given undirected graph G, the minimum rank of G is defined to be the smallest possible rank over all real symmetric matrices A whose (i, j )th entry is nonzero whenever i / = j and {i, j } is an edge in G. In this work we consider joins and unions of graphs, and characterize the minimum rank o
The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied exte
## Abstract We determine necessary and sufficient conditions for a complete multipartite graph to admit a set of 1βfactors whose union is the whole graph and, when these conditions are satisfied, we determine the minimum size of such a set. Β© 2008 Wiley Periodicals, Inc. J Graph Theory 58:239β250,
For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n Γ n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ