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- W567278446 abstract "The Minimum Rank of Schemes on Graphs William Nelson Sexton Department of Mathematics, BYU Master of Science Let G be an undirected graph on n vertices and let S(G) be the class of all real-valued symmetric n× n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let V = {1, 2, . . . , n} be the vertex set of G. A scheme on G is a function f : V → {0, 1}. Given a scheme f on G, there is an associated class of matrices Sf (G) = {A ∈ S(G)|aii = 0 if and only if f(i) = 0}. A scheme f is said to be constructible if there exists a matrix A ∈ Sf (G) with rankA = min{rankM |M ∈ S(G)}. We explore properties of constructible schemes and give a complete classification of which schemes are constructible for paths and cycles. We also consider schemes on complete graphs and show the existence of a graph for which every possible scheme is constructible." @default.
- W567278446 created "2016-06-24" @default.
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- W567278446 date "2014-01-01" @default.
- W567278446 modified "2023-09-23" @default.
- W567278446 title "The Minimum Rank of Schemes on Graphs" @default.
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