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Laplacian spectral characterization of some graph join

Author

Listed:
  • Lizhu Sun

    (Harbin Engineering University)

  • Wenzhe Wang

    (Harbin Engineering University)

  • Jiang Zhou

    (Harbin Engineering University
    Harbin Engineering University)

  • Changjiang Bu

    (Harbin Engineering University)

Abstract

For two disjoint graphs G and H, the join of G and H, denoted by G ∨ H, is the graph obtained from G ∪ H by joining each vertex of G to each vertex of H. A graph is said to be DLS if there is no other non-isomorphic graph with the same Laplacian spectrum. For a connected DLS graph G with a cut vertex, we prove that G ∨ K r is DLS, where K r is a complete graph. For a disconnected DLS graph G with n ⩾ 10 vertices and m ⩽ n — 4 edges, we show that G ∨ (K r — e) is DLS, where K r — e is the graph obtained by deleting one edge of K r . Applying these results we can obtain new DLS graphs.

Suggested Citation

  • Lizhu Sun & Wenzhe Wang & Jiang Zhou & Changjiang Bu, 2015. "Laplacian spectral characterization of some graph join," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(3), pages 279-286, June.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:3:d:10.1007_s13226-015-0124-9
    DOI: 10.1007/s13226-015-0124-9
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2009. "Developments on spectral characterizations of graphs," Other publications TiSEM 7b5eb8d4-dfc2-4392-bb3f-4, Tilburg University, School of Economics and Management.
    2. van Dam, E.R. & Haemers, W.H., 2003. "Which graphs are determined by their spectrum?," Other publications TiSEM a9a1857e-13ce-4da7-bcca-b, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Xihe Li & Ligong Wang & Shangyuan Zhang, 2018. "The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 113-127, March.
    2. B. R. Rakshith, 2022. "Signless Laplacian spectral characterization of some disjoint union of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 233-245, March.

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