English

Laplacian Spectral Determination of Path-Friendship Graphs

Combinatorics 2019-03-28 v1

Abstract

A graph GG is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to GG. 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