On Several Parameters of Super Line Graph L 2 (G).

The super line graph of index r, denoted by L r (G) , is defined for any graph G with at least r edges. Its vertices are the sets of r edges of G, and two such sets are adjacent if an edge of one is adjacent to an edge of the other. In this paper, we give an explicit characterization for all graphs G with L 2 (G) being a complete graph. We present lower bounds for the clique number and chromatic number of L 2 (G) for several classes of graphs. In addition, bounds for the domination number of L 2 (G) are established in terms of the domination number of the line graph L (G) of a graph. A number of related problems on L 2 (G) are proposed for a further study. [ABSTRACT FROM AUTHOR]