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Old and new results on algebraic connectivity of graphs

โœ Scribed by Nair Maria Maia de Abreu

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
272 KB
Volume
423
Category
Article
ISSN
0024-3795

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We find an upper bound on the algebraic connectivity of graphs of various genus. We begin by showing that for fixed k 1, the graph of genus k of largest algebraic connectivity is a complete graph. We then find an upper bound for noncomplete graphs of a fixed genus k 1 and we determine the values of

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In this paper, we first determine that the first four trees of order n 9 with the smallest algebraic connectivity are P n , Q n , W n and Z n with ฮฑ(P n ) < ฮฑ(Q n ) < ฮฑ(W n ) < ฮฑ(Z n ) < ฮฑ(T ), where T is any tree of order n other than P n , Q n , W n , and Z n . Then we consider the effect on the L