Wiener index versus maximum degree in trees

Authors:
Miranca Fischermann;Arne Hoffmann;Dieter Rautenbach;László Székely;Lutz Volkmann
Affiliations:
Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany;Lehrstuhl C für Mathematik, RWTH-Aachen, 52056 Aachen, Germany;Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany and Equipe Combinatoire, UFR 921, 175 rue de Chevaleret, 75013 Paris, France;Department of Mathematics, University of South Carolina, Columbia, SC;Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2002

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Abstract

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. In this paper, we characterize the trees which minimize the Wiener index among all trees of given order and maximum degree and the trees which maximize the Wiener index among all trees of given order that have only vertices of two different degrees.