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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Spectra, Energy and Laplacian Energy of Strong Double Graphs
verfasst von : Shariefuddin Pirzada, Hilal A. Ganie
Erschienen in: Mathematical Technology of Networks
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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.