Turán Graphs, Stability Number, and Fibonacci Index
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
On the extremal Merrifield-Simmons index and Hosoya index of quasi-tree graphs
Discrete Applied Mathematics
Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
On the number of independent subsets in trees with restricted degrees
Mathematical and Computer Modelling: An International Journal
Energy, Hosoya index and Merrifield-Simmons index of trees with prescribed degree sequence
Discrete Applied Mathematics
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The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has already been investigated by many authors. In view of the applications of this graph parameter, trees of restricted degree are of particular interest. In the current article, we give a characterization of the trees with given maximum degree which maximize the number of independent subsets, and show that these trees also minimize the number of independent edge subsets. The structure of these trees is quite interesting and unexpected: it can be described by means of a novel digital system—in the case of maximum degree 3, we obtain a binary system using the digits 1 and 4. The proof mainly depends on an exchange lemma for branches of a tree. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 49–68, 2008 Dedicated to Prof. Robert Tichy on the occasion of his 50th birthday. This article was written while C. Heuberger was a visitor at the Center of Experimental Mathematics at the University of Stellenbosch. He thanks the center for its hospitality.