abs_vol20_pp610-620. 28KB Jun 04 2011 12:05:48 AM

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ELA

THE SUN GRAPH IS DETERMINED BY ITS SIGNLESS

LAPLACIAN SPECTRUM

∗

M. MIRZAKHAH† _AND _{D. KIANI}†‡

Abstract. For a simple undirected graph G, the corresponding signless Laplacian matrix is defined asD₍G_{) +}A₍G_{) in which}D₍G_{) and}A₍G_{) are degree matrix and adjacency matrix of}G_,

respectively. The graph G is said to be determined by its signless Laplacian spectrum, if any graph having the same signless Laplacian spectrum asG_{is isomorphic to}G_{. Also the}_{Sun graph}_{of order}

2n_{is a cycle}Cnwith an edge terminating in a pendent vertex attached to each vertex. Among other things, one result in this paper is that the Sun graphs are determined by their signless Laplacian spectrum.

Key words. Sun graph, Signless Laplacian matrix, Cospectral graphs.

AMS subject classifications. 05C50, 05C90.

∗_{Received by the editors March 5, 2010. Accepted for publication on July 31, 2010. Handling}

Editor: Stephen Kirkland.

†_{Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir}

University of Technology (Tehran Polytechnic), P.O. Box 15875-4413, Tehran, Iran (mirzakhah@aut.ac.ir, dkiani@aut.ac.ir).

‡_{School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box}

19395-5746, Tehran, Iran. Supported in part by IPM Grant No. 89050116 and National Foundation of Elites.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 610-620, September 2010