The paper asserts jellyfish graphs are determined by Laplacian and signless Laplacian spectra, but the Laplacian proof uses a false spectral radius bound and the signless proof has an unproved step.
Laplacian Spectral Determination of Path-Friendship Graphs
1 Pith paper cite this work. Polarity classification is still indexing.
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Pith paper citing it
abstract
A graph $G$ is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to $G$. van Dam and Haemers (2003) conjectured that almost all graphs have this property, but that is known to be the case only for a very few families. In some recent papers it is proved that the friendship graphs and starlike trees are DLS. If a friendship graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a path-friendship graph. In this paper, it is proved that the path-friendship graphs are also DLS.
fields
math.CO 1years
2019 1verdicts
REJECT 1representative citing papers
citing papers explorer
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No two Jellyfish graphs are L-cospectral and Q-cospectral
The paper asserts jellyfish graphs are determined by Laplacian and signless Laplacian spectra, but the Laplacian proof uses a false spectral radius bound and the signless proof has an unproved step.