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Full-Text Articles in Physical Sciences and Mathematics
Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy
Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy
Faculty Publications
Let F be a finite field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with p^t elements, p does not = 2, it is shown that mr(F,G) ≤ 2 if and only if the complement of G is the join of a complete graph with either the union of at most …