Laplacian spectral characterization of some graph join

Lizhu Sun, Wenzhe Wang, Jiang Zhou () and Changjiang Bu
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Lizhu Sun: Harbin Engineering University
Wenzhe Wang: Harbin Engineering University
Jiang Zhou: Harbin Engineering University
Changjiang Bu: Harbin Engineering University

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 3, 279-286

Abstract: 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.

Keywords: Cospectral graphs; Laplacian spectrum; spectral characterization; join (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13226-015-0124-9

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