A New Upper Bound for the d-dimensional Algebraic Connectivity of Arbitrary Graphs

Juan F. Presenza,Ignacio Mas,Juan I. Giribet,J. Ignacio Alvarez-Hamelin

arxiv（2022）

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摘要

In this paper we show that the $d$-dimensional algebraic connectivity of an arbitrary graph $G$ is bounded above by its $1$-dimensional algebraic connectivity, i.e., $a_d(G) \leq a_1(G)$, where $a_1(G)$ corresponds the well-studied second smallest eigenvalue of the graph Laplacian.

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关键词

arbitrary graphs,connectivity,new upper bound,d-dimensional

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