Unicyclic Graphs with equal Laplacian Energy
Eliseu Fritscher, Carlos Hoppen, Vilmar Trevisan
TL;DR
This paper introduces a novel graph operation that generates families of unicyclic graphs with equal Laplacian energy but different spectra, expanding understanding of spectral graph properties.
Contribution
It presents a new graph operation that produces noncospectral unicyclic graphs with identical Laplacian energy, a significant advance in spectral graph theory.
Findings
Constructed families of noncospectral unicyclic graphs with equal Laplacian energy.
Established a relationship between Laplacian eigenvalues of input and output graphs.
Demonstrated the existence of order √n noncospectral graphs with the same Laplacian energy.
Abstract
We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of order (square root of n) noncospectral unicyclic graphs on n vertices with the same Laplacian energy.
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