Abstract
The rank of the adjacency matrix of a graph is bounded above by the numberof distinct non-zero rows of that matrix. In general, the rank is lower than thisnumber because there may be some non-trivial linear combination of the rows equalto zero. We show the somewhat surprising result that this never occurs for the classof cographs. Therefore, the rank of a cograph is equal to the number of distinctnon-zero rows of its adjacency matrix.
| Original language | English |
|---|---|
| Pages (from-to) | online - approx 5-20pp |
| Journal | The Electronic Journal of Combinatorics |
| Volume | 10 |
| Publication status | Published - 2003 |