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The algebraic connectivity of graphs under perturbation

โœ Scribed by Ji-Ming Guo

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
160 KB
Volume
433
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

In this paper, we investigate how the algebraic connectivity of a connected graph behaves when the graph is perturbed by separating or grafting an edge.

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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