The distinguishing number of the iterated line graph
Combinatorics
2007-05-23 v1
Abstract
We show that for all simple graphs G other than the cycles C_3,C_4,C_5, and the claw K_1,3 there exists a K > 0 such that whenever k > K the k-th iterate of the line graph can be distinguished by at most two colors. Additionally we determine, for trees, when the distinguishing number of the line graph of T is greater than the distinguishing number of T.
Cite
@article{arxiv.math/0509296,
title = {The distinguishing number of the iterated line graph},
author = {Ian Shipman},
journal= {arXiv preprint arXiv:math/0509296},
year = {2007}
}
Comments
10 pages, 2 figures