| dc.contributor.author | Kranda, Daniel Joseph | |
| dc.description.abstract | It can be shown that any symmetric (0, 1)-matrix A with tr A = 0 can be interpreted as the adjacency matrix of a simple, finite graph. The square of an adjacency matrix A2 = (si1) has the property that Sij represents the number of walks of length two from vertex i to vertex j. With this information, the motivating question behind this paper was to determine what conditions on a matrix S are needed to have S = A(G)2 for some graph G. Structural results imposed by the matrix S include detecting bipartiteness or connectedness, counting four cycles and determining plausible neighborhoods of vertices. Some characterizations will be given and the problem of when S represents several non-isomorphic graphs is also explored. | en_US |
| dc.publisher | North Dakota State University | en_US |
| dc.rights | NDSU policy 190.6.2 | en_US |
| dc.title | The Square of Adjacency Matrices | en_US |
| dc.type | Thesis | en_US |
| dc.date.accessioned | 2023-11-17T18:41:24Z | |
| dc.date.available | 2023-11-17T18:41:24Z | |
| dc.date.issued | 2011 | |
| dc.identifier.uri | https://hdl.handle.net/10365/33250 | |
| dc.subject.lcsh | Matrices. | en_US |
| dc.subject.lcsh | Graph theory. | en_US |
| dc.rights.uri | https://www.ndsu.edu/fileadmin/policy/190.pdf | en_US |
| ndsu.degree | Master of Science (MS) | en_US |
| ndsu.college | Science and Mathematics | en_US |
| ndsu.department | Mathematics | en_US |
| ndsu.program | Mathematics | en_US |
| ndsu.advisor | Shreve, Warren E. | |
