Resonance Graph of Perfect Matchings
| dc.contributor.advisor | Ye, Dong | |
| dc.contributor.author | Aluoch, James | |
| dc.contributor.committeemember | Stephens, Chris | |
| dc.contributor.committeemember | Zha, Xiaoya | |
| dc.contributor.department | Basic & Applied Sciences | en_US |
| dc.date.accessioned | 2019-06-13T18:00:16Z | |
| dc.date.available | 2019-06-13T18:00:16Z | |
| dc.date.issued | 2019 | |
| dc.date.updated | 2019-06-13T18:00:18Z | |
| dc.description.abstract | Let G be a graph with perfect matchings and let C be a set of linearly independent even cycles of G of width at most 2. The resonance graph R(G, C) is a graph with the vertex set M a subset of M(G) such that two vertices Mi and Mj are adjacent if and only if the direct sum of Mi and Mj is E(c) for some cycle c in C. In this paper, we extend the results obtained by Tratnik and Ye to general graphs. Particulary, we show that the resonance graph of every graph with perfect matchings with respect to a set of linearly independent even cycles of width at most 2 is bipartite and each connected component of the resonance graph is an induced cubical graph. | |
| dc.description.degree | M.S. | |
| dc.identifier.uri | http://jewlscholar.mtsu.edu/xmlui/handle/mtsu/5881 | |
| dc.language.rfc3066 | en | |
| dc.publisher | Middle Tennessee State University | |
| dc.subject | Mathematics | |
| dc.thesis.degreegrantor | Middle Tennessee State University | |
| dc.title | Resonance Graph of Perfect Matchings |