Algebraic connectivity of connected graphs with fixed number of pendant vertices

Details Algebraic connectivity of connected graphs with fixed number of pendant vertices Algebraic connectivity of connected graphs with fixed number of pendant vertices

2010-03-24

arxiv.org/abs/1003.4646v1

Mathematics

Combinatorics

14 pages, 11 figures

Scientific paper

In this paper we consider the following problem: Over the class of all simple
connected graphs of order $n$ with $k$ pendant vertices ($n,k$ being fixed),
which graph maximizes (respectively, minimizes) the algebraic connectivity? We
also discuss the algebraic connectivity of unicyclic graphs.

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