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The distinguishing number of the iterated line graph

Ian Shipman
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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.

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Ian Shipman. 2005-09-14. The distinguishing number of the iterated line graph. https://arxiv.org/abs/math/0509296

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