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The spectra and the signless Laplacian spectra of graphs with pockets

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  • Cui, Shu-Yu
  • Tian, Gui-Xian

Abstract

Let G[F, Vk, Hv] be the graph with k pockets, where F is a simple graph of order n ≥ 1, Vk={v1,…,vk} is a subset of the vertex set of F and Hv is a simple graph of order m ≥ 2, v is a specified vertex of Hv. Also let G[F, Ek, Huv] be the graph with k edge-pockets, where F is a simple graph of order n ≥ 2, Ek={e1,…,ek} is a subset of the edge set of F and Huv is a simple graph of order m ≥ 3, uv is a specified edge of Huv such that Huv−u is isomorphic to Huv−v. In this paper, we obtain some results describing the signless Laplacian spectra of G[F, Vk, Hv] and G[F, Ek, Huv] in terms of the signless Laplacian spectra of F, Hv and F, Huv, respectively. In addition, we also give some results describing the adjacency spectrum of G[F, Vk, Hv] in terms of the adjacency spectra of F, Hv. Finally, as many applications of these results, we construct infinitely many pairs of signless Laplacian (resp. adjacency) cospectral graphs.

Suggested Citation

  • Cui, Shu-Yu & Tian, Gui-Xian, 2017. "The spectra and the signless Laplacian spectra of graphs with pockets," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 363-371.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:363-371
    DOI: 10.1016/j.amc.2017.07.056
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
    2. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "The normalized Laplacian spectrum of subdivisions of a graph," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 250-256.
    3. Das, Kinkar Ch. & Liu, Muhuo, 2017. "Kite graphs determined by their spectra," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 74-78.
    4. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "On the spectrum of the normalized Laplacian of iterated triangulations of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1123-1129.
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    Cited by:

    1. R. Pavithra & R. Rajkumar, 2021. "Spectra of M-edge rooted product of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 1235-1255, December.

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