Signless Laplacian spectral determinations of some multicone graphs

Document Type : Research Articles

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1 Department of Mathematics, Faculty of Sciences, Lorestan , Khorram abad, Iran.

2 Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran

Abstract

If a clique and a regular graph are joined together the resulting graph is called a multicone graph. A graph $G$ is said to be determined by the spectrum of its signless Laplacian matrix (DQS, for short) if every graph with the same Laplacian spectrum is isomorphic to $G$. It is proved that all the multicone graphs $K_r\bigtriangledown sK_t$, except for $K_r\bigtriangledown 3K_1$, are DQS, where $K_r$ denots a complete graph with $r\geq 1$ vertices. Consequently, by using these results we give a response to an open problem in [24].

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