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
Recommended Citation
Bapat, Ravindra B.; Lal, A. K.; and Pati, S., "Some Observations on Algebraic Connectivity of Graphs" (2023). Book Chapters. 189.
https://digitalcommons.isical.ac.in/book-chapters/189