On the d-dimensional algebraic connectivity of graphs

Alan Lew*, Eran Nevo, Yuval Peled, Orit E. Raz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The d-dimensional algebraic connectivity ad(G) of a graph G = (V,E), introduced by Jordán and Tanigawa, is a quantitative measure of the d-dimensional rigidity of G that is defined in terms of the eigenvalues of stiffness matrices (which are analogues of the graph Laplacian) associated to mappings of the vertex set V into ℝ d. Here, we analyze the d-dimensional algebraic connectivity of complete graphs. In particular, we show that, for d ≥ 3, ad(Kd+1) = 1, and for n ≥ 2d, ⌈n2d⌉−2d+1≤ad(Kn)≤2n3(d−1)+13.

Original languageAmerican English
Pages (from-to)479-511
Number of pages33
JournalIsrael Journal of Mathematics
Volume256
Issue number2
DOIs
StatePublished - Sep 2023

Bibliographical note

Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.

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