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The main aim of this study is to characterize new classes of multicone graphs which are determined by their adjacency spectra, their Laplacian spectra, their complement with respect to signless Laplacian spectra and their complement with respect to their adjacency spectra. A multicone graph is defined to be the join of a clique and a regular graph. If n is a positive integer, a friendship graph $F_n$ consists of n edge-disjoint triangles that all of them meet in one vertex. It is proved that any connected graph cospectral to a multicone graph $F_n{\nabla}F_n=K_2{\nabla}nK_2{\nabla}nK_2$ is determined by its adjacency spectra as well as its Laplacian spectra. In addition, we show that if $n{\neq}2$, the complement of these graphs are determined by their adjacency spectra. At the end of the paper, it is proved that multicone graphs $F_n{\nabla}F_n=K_2{\nabla}nK_2{\nabla}nK_2$ are determined by their signless Laplacian spectra and also we prove that any graph cospectral to one of multicone graphs $F_n{\nabla}F_n$ is perfect.
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참고문헌 (42)
참고문헌 신청
A.Z. Abdian / 2015 / On new classes of multicone graphs determined by their spectrums / Alg. Struc. Appl 2:23~34
A.Z. Abdian / 2016 / Graphs which are determined by their spectrum / Konuralp. J. Math 4:34~41
A.Z. Abdian / 2016 / Two classes of multicone graphs determined by their spectra / J. Math. Ext 10:111~121
A.Z. Abdian / 2017 / Graphs cospectral with multicone graphs Kw ∇ L(P) / TWMS. J. App. and Eng. Math. 7:181~187
A.Z. Abdian / The spectral determinations of the multicone graphs Kw ∇ P / arXiv:1706.02661
A.Z. Abdian / 2016 / Graphs which are determined by their spectrum / Konuralp. J. Math 4:34~41
A.Z. Abdian / 2016 / Two classes of multicone graphs determined by their spectra / J. Math. Ext 10:111~121
A.Z. Abdian / 2017 / Graphs cospectral with multicone graphs Kw ∇ L(P) / TWMS. J. App. and Eng. Math. 7:181~187
A.Z. Abdian / The spectral determinations of the multicone graphs Kw ∇ P / arXiv:1706.02661
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