A linear-programming approach to the generalized Randić index

Authors:
Miranca Fischermann;Arne Hoffmann;Dieter Rautenbach;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;Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

The generalized Randic´ index Rα(G) of a graph G is the sum of (dG(u)dG(v))α over all edges uv of G. Using a linear-programming approach, we establish results on graphs with a given number of vertices and edges and a bounded maximum degree that are of minimum generalized Randic´ index for α ∈ {- ½, - 1}.