The distinguishing number of the iterated line graph
Abstract
We show that for all simple graphs G other than the cycles C3,C4,C5, and the claw K1,3 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.
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