Abstract
For a graph G with vertex set \(V (G)\,=\,\{v_{1},v_{2},\cdots \,,v_{n}\}\), the strong double graph SD(G) is a graph obtained by taking two copies of G and joining each vertex v i in one copy with the closed neighbourhood N[v i ] = N(v i ) ∪{ v i } of corresponding vertex in another copy. In this paper, we study spectra, energy and Laplacian energy of the graph SD(G). We also obtain some new families of equienergetic and L-equienergetic graphs, and an infinite family of graphs G for which LE(G) < E(G). We derive a formula for the number of spanning trees of SD(G) in terms of the number of spanning trees of G.
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Pirzada, S., Ganie, H.A. (2015). Spectra, Energy and Laplacian Energy of Strong Double Graphs. In: Mugnolo, D. (eds) Mathematical Technology of Networks. Springer Proceedings in Mathematics & Statistics, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-319-16619-3_12
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DOI: https://doi.org/10.1007/978-3-319-16619-3_12
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