The sun graph is determined by its signless Laplacian spectrum

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Maryam Mirzakhah
Dariush Kiani


For a simple undirected graph G, the corresponding signless Laplacian matrix is defined as D(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 as G is isomorphic to G. Also the Sun graph of order 2n is a cycle Cn with 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.

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