The structure of super line graphs

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The structure of super line graphs
For a given graph G = (V, E) and a positive integer k, the super line graph of index k of G is the graph Sk(G) which has for vertices all the k-subsets of E(G), and two vertices S and T are adjacent whenever there exist s ∈ S and t ∈ T such that s and t share a common vertex. In the super line multigraph Lk(G) we have an adjacency for each such occurrence. We give a formula to find the adjacency matrix of Lk(G). If G is a regular graph, we calculate all the eigenvalues of Lk(G) and their multiplicities. From those results we give an upper bound on the number of isolated vertices.
Jay Bagga, Daniela Ferrero
Added 25 Jun 2010
Updated 25 Jun 2010
Type Conference
Year 2005
Authors Jay Bagga, Daniela Ferrero
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