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arXiv · 2209.14893

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
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Abstract

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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Juan F. Presenza, Ignacio Mas, Juan I. Giribet, J. Ignacio Alvarez-Hamelin. 2022-09-29. A New Upper Bound for the d-dimensional Algebraic Connectivity of Arbitrary Graphs. https://arxiv.org/abs/2209.14893

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