Some Observations on Algebraic Connectivity of Graphs

Document Type

Book Chapter

Publication Title

Indian Statistical Institute Series

Abstract

Let G be a connected simple graph and L(G) be its Laplacian matrix. Let v be a cut vertex and B be a branch at v. Assume that v1 is the only vertex in B adjacent to v. Let P be a path that starts at v1 while staying inside B. It is shown that the algebraic connectivity decreases if we do an appropriate sliding operation along the path. Similar results for trees were known decades ago. This general result was believed to be true, but it was never established.

First Page

177

Last Page

190

DOI

10.1007/978-981-99-2310-6_9

Publication Date

1-1-2023

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