Maximum and minimum degree in iterated line graphs
Metadata Field | Value | Language |
---|---|---|
dc.contributor.advisor | Hoffman, Dean | |
dc.contributor.author | Aggarwal, Manu | |
dc.date.accessioned | 2013-06-13T15:59:57Z | |
dc.date.available | 2013-06-13T15:59:57Z | |
dc.date.issued | 2013-06-13 | |
dc.identifier.uri | http://hdl.handle.net/10415/3663 | |
dc.description.abstract | In this thesis we analyze two papers, both by Dr. Stephen G. Hartke and Dr. Aparna W. Higginson, on maximum and minimum degrees of a graph $G$ under iterated line graph operations. Let $\Delta_{k}$ and $\delta_{k}$ denote the minimum and the maximum degrees, respectively, of the $k^{th}$ iterated line graph $L^{k}(G)$. It is shown that if $G$ is not a path, then, there exist integers $A$ and $B$ such that for all $k>A$, $\Delta_{k+1}=2\Delta_{k}-2$ and for all $k>B$, $\delta_{k+1}=2\delta_{k}-2$. | en_US |
dc.rights | EMBARGO_NOT_AUBURN | en_US |
dc.subject | Mathematics and Statistics | en_US |
dc.title | Maximum and minimum degree in iterated line graphs | en_US |
dc.type | thesis | en_US |
dc.embargo.length | NO_RESTRICTION | en_US |
dc.embargo.status | NOT_EMBARGOED | en_US |