Chenette, Nathan L.; Droms, Sean V.; Hogben, Leslie; Mikkelson, Rana; Pryporova, Olga
Minimum rank of a tree over an arbitrary field
Electron. J. Linear Algebra 16, 183-186, electronic only (2007)
Summary
Summary: For a field F and graph G of order n, the minimum rank of G over F is defined to be the smallest possible rank over all symmetric matrices A 2 F n*n whose (i, j)th entry (for i 6= j) is nonzero whenever ${i, j}$ is an edge in G and is zero otherwise. It is shown that the minimum rank of a tree is independent of the field.
