# On eigenspaces of some compound complex unit gain graphs

Document Type : Workshop on Graphs, Topology and Topological Groups, Cape Town, South Africa

Authors

Maurizio Brunetti Dipartimento di Matematica e Applicazioni, Università di Napoli ‘Federico II’, Naples, Italy

Abstract

Let $\mathbb T$ be the multiplicative group of complex units, and let $L(\Phi)$ denote the Laplacian matrix of a nonempty $\mathbb{T}$-gain graph $\Phi=(\Gamma, \mathbb{T}, \gamma)$. The gain line graph $\mathcal L(\Phi)$ and the gain subdivision graph $\mathcal S(\Phi)$ are defined up to switching equivalence. We discuss how the eigenspaces determined by the adjacency eigenvalues of $\mathcal L(\Phi)$ and $\mathcal S(\Phi)$ are related with those of $L(\Phi)$.

Keywords

Main Subjects

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