Maximum Wiener Index of Trees With Given Segment Sequence
MATCH Communications in Math and Computer Chemistry
A segment of a tree is a path whose ends are branching vertices (vertices of degree greater than 2) or leaves, while all other vertices have degree 2. The lengths of all the segments of a tree form its segment sequence. In this note we consider the problem of maximizing the Wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent paper on the subject. We show that the maximum is always obtained for a so-called quasi-caterpillar, and we also further characterize its structure.
Andriantiana, Eric Ould Dadah, Stephan G. Wagner, Hua Wang.
"Maximum Wiener Index of Trees With Given Segment Sequence."
MATCH Communications in Math and Computer Chemistry, 75 (1): 1-9.