@article {
author = {Abdollahi, Alireza and Janbaz, Shahrooz},
title = {Connected graphs cospectral with a friendship graph},
journal = {Transactions on Combinatorics},
volume = {3},
number = {2},
pages = {17-20},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2014.4975},
abstract = {Let $n$ be any positive integer, the friendship graph $F_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. A graph $G$ is called cospectral with a graph $H$ if their adjacency matrices have the same eigenvalues. Recently in \href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org /pdf/1310.6529v1.pdf} it is proved that if $G$ is any graph cospectral with $F_n$ ($n\neq 16$), then $G\cong F_n$. Here we give a proof of a special case of the latter: Any connected graph cospectral with $F_n$ is isomorphic to $F_n$. Our proof is independent of ones given in \href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} and the proofs are based on our recent results given in [Trans. Comb., 2 no. 4 (2013) 37-52.] using an upper bound for the largest eigenvalue of a connected graph given in [J. Combinatorial Theory Ser. B, 81 (2001) 177-183.].},
keywords = {Friendship graphs,cospectral graphs,adjacency eigenvalues,spectral radius},
url = {https://toc.ui.ac.ir/article_4975.html},
eprint = {https://toc.ui.ac.ir/article_4975_b084afb2f80121996ddeade80cc392f1.pdf}
}