Forbidden Minors for the Class of Graphs
نویسندگان
چکیده
For a given simple graph G, S(G) is defined to be the set of real symmetric matrices A whose (i, j)th entry is nonzero whenever i 6= j and ij is an edge in G. In [2], ξ(G) is defined to be the maximum corank (i.e., nullity) among A ∈ S(G) having the Strong Arnold Property; ξ is used to study the minimum rank/maximum eigenvalue multiplicity problem for G. Since ξ is minor monotone, the graphs G such that ξ(G) ≤ k can be described by a finite set of forbidden minors. We determine the forbidden minors for ξ(G) ≤ 2 and present an application of this characterization to computation of minimum rank among matrices in S(G).
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