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## Maximum and minimum degree in iterated line graphs

##### Date

2013-06-13##### Author

Aggarwal, Manu

##### Type of Degree

thesis##### Department

Mathematics and Statistics##### Metadata

Show full item record##### 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 $k>B$, $\delta_{k+1}=2\delta_{k}-2$.