Geodesic
The rank of a cograph
The electronic journal of combinatorics, Tome 10 (2003)
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The rank of the adjacency matrix of a graph is bounded above by the number of distinct non-zero rows of that matrix. In general, the rank is lower than this number because there may be some non-trivial linear combination of the rows equal to zero. We show the somewhat surprising result that this never occurs for the class of cographs. Therefore, the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix.
DOI : 10.37236/1751
Classification : 05C50
Mots-clés : adjacency matrix 
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     author = {Gordon F. Royle},
     title = {The rank of a cograph},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1751},
     zbl = {1024.05058},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1751/}
}
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Gordon F. Royle. The rank of a cograph. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1751

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