TY - JOUR
T1 - On the d-dimensional algebraic connectivity of graphs
AU - Lew, Alan
AU - Nevo, Eran
AU - Peled, Yuval
AU - Raz, Orit E.
N1 - Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.
PY - 2023/9/1
Y1 - 2023/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85173760337&partnerID=8YFLogxK
U2 - 10.1007/s11856-023-2519-3
DO - 10.1007/s11856-023-2519-3
M3 - Article
AN - SCOPUS:85173760337
SN - 0021-2172
VL - 256
SP - 479
EP - 511
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -