connected graphs cospectral with a friendship graph

نویسندگان

alireza abdollahi

shahrooz janbaz

چکیده

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 $f_n$ ($nneq 16$), then $gcong f_n$. in this note, 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 [{em trans. comb.}, {bf 2} no. 4 (2013) 37-52.] using an upper bound for the largest eigenvalue of a connected graph given in[{em j. combinatorial theory ser. b} {bf 81} (2001) 177-183.].

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عنوان ژورنال:
transactions on combinatorics

ناشر: university of isfahan

ISSN 2251-8657

دوره 3

شماره 2 2014

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