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.

• Type: Conference
• Year: 2005
• Where: ISPAN
• Authors: Jay Bagga, Daniela Ferrero
• Keywords: Distributed And Parallel Computing, ISPAN 2005, Positive Integer, Super Line, Super Line Graph