CONNECTED GRAPHS COSPECTRAL WITH A FRIENDSHIP GRAPH

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ABDOLLAHI A.; JANBAZI SH.

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Journal: TRANSACTIONS ON COMBINATORICS Year:2014 | Volume:3 | Issue:2 Page(s): 17-20

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Information Journal Paper

Title

CONNECTED GRAPHS COSPECTRAL WITH A FRIENDSHIP GRAPH

Author(s)

ABDOLLAHI A. | JANBAZI SH. | Issue Writer Certificate

Keywords

FRIENDSHIP GRAPHS

COSPECTRAL GRAPHS

ADJACENCY EIGENVALUES

SPECTRAL RADIUS

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 ¹16), 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.].

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APA: Copy

ABDOLLAHI, A., & JANBAZI, SH.. (2014). CONNECTED GRAPHS COSPECTRAL WITH A FRIENDSHIP GRAPH. TRANSACTIONS ON COMBINATORICS, 3(2), 17-20. SID. https://sid.ir/paper/636842/en

Vancouver: Copy

ABDOLLAHI A., JANBAZI SH.. CONNECTED GRAPHS COSPECTRAL WITH A FRIENDSHIP GRAPH. TRANSACTIONS ON COMBINATORICS[Internet]. 2014;3(2):17-20. Available from: https://sid.ir/paper/636842/en

IEEE: Copy

A. ABDOLLAHI, and SH. JANBAZI, “CONNECTED GRAPHS COSPECTRAL WITH A FRIENDSHIP GRAPH,” TRANSACTIONS ON COMBINATORICS, vol. 3, no. 2, pp. 17–20, 2014, [Online]. Available: https://sid.ir/paper/636842/en

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