Laplacian Spectral Determination of Path-Friendship Graphs
Combinatorics
2019-03-28 v1
Abstract
A graph is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to . 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.
Keywords
Cite
@article{arxiv.1903.11121,
title = {Laplacian Spectral Determination of Path-Friendship Graphs},
author = {A. Z. Abdian and A. R. Ashrafi and L. W. Beineke and M. R. Oboudi},
journal= {arXiv preprint arXiv:1903.11121},
year = {2019}
}
Comments
11 Pages