Geodesic
Maximal buttonings of trees
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 415-420

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A buttoning of a tree that has vertices v_1, v_2, . . ., v_n is a closed walk that starts at v_1 and travels along the shortest path in the tree to v_2, and then along the shortest path to v_3, and so forth, finishing with the shortest path from v_n to v_1. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees.
Keywords: centroid, graph metric, tree, walk, Wiener distance 
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Short, Ian. Maximal buttonings of trees. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 415-420. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a14/