Researcher(s)
- Jarrod Dunn, Mathematics, University of Delaware
Faculty Mentor(s)
- Dominique Guillot, Mathematical Sciences, University of Delaware
Abstract
We consider symmetric, n x n matrices whose entries are all 0 and 1 in the field of integers modulo a prime number, p. We are interested in determining the admissible patterns that lead to a positive semidefinite matrix (i.e., all the principal minors of the matrix are equal to the square of some integer modulo p). Identifying such matrices with the adjacency matrix of a graph, we seek to determine which graphs yield a positive semidefinite matrix. We identify several subgraphs that are not admissible for obtaining a positive semidefinite adjacency matrix. We also observe that whether p is congruent to 1 or 3 modulo 4 plays an important role in that problem.