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Laplacian spectral characterization of some graph join

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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.

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Authors and Affiliations

  1. College of Science, Harbin Engineering University, Harbin, 150001, P R China

    Lizhu Sun, Wenzhe Wang, Jiang Zhou & Changjiang Bu

  2. College of Computer Science and Technology, Harbin Engineering University, Harbin, 150001, P R China

    Jiang Zhou

Authors
  1. Lizhu Sun
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  2. Wenzhe Wang
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  3. Jiang Zhou
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  4. Changjiang Bu
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Correspondence to Jiang Zhou.

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Sun, L., Wang, W., Zhou, J. et al. Laplacian spectral characterization of some graph join. Indian J Pure Appl Math 46, 279–286 (2015). https://doi.org/10.1007/s13226-015-0124-9

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  • DOI: https://doi.org/10.1007/s13226-015-0124-9

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