Title of article :
Connected graphs cospectral with a Friendship graph
Author/Authors :
عبدالهي ، عليرضا نويسنده Abdollahi, A , جانباز، شهروز نويسنده Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran Janbaz, Shahrooz
Issue Information :
فصلنامه با شماره پیاپی 0 سال 2014
Abstract :
Let n be any positive integer, the friendship graph Fn 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 http://arxiv.org/pdf/1310.6529v1.pdf it is proved that
if G is any graph cospectral with Fn (n 6= 16), then G = Fn. Here we give a proof of a special case
of the latter: Any connected graph cospectral with Fn is isomorphic to Fn. Our proof is independent
of ones given in 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.].
Journal title :
Transactions on Combinatorics
Journal title :
Transactions on Combinatorics