View Proposal #202
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| ID | 202 |
|---|---|
| First Name | Luz |
| Last Name | De Alba Guerra |
| Institution | Drake University |
| Speaker Category | faculty |
| Title of Talk | Minimum Rank of Powers of Some Special Graphs |
| Abstract | For an n x n symmetric matrix A the graph of A, G(A) =(V, E) is a simple undirected graph with vertex set {1, 2, ..., n }, where {i, j } is in E, if and only if a_{ij} is not 0. For a graph G, with vertex set V = {1, 2, ..., n }, and edge set E, the r-th power of G is the graph G^r = (V, F), where {u, v } is in F if and only if there is a walk of length r from u to v. The minimum rank of a graph G is mr(G) = min{ rank(A) : A = A^T, and G(A) = G }. In this talk we determine the minimum rank of certain powers of two special families of graphs: paths and trees in general. We will also present a onjecture on the minimum rank of powers of cycles. |
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| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | |
| Overhead Needed? | |
| Software requests | |
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| Date Submitted | 4/3/2007 |
| Year | 2007 |