Independence and Cycles in Super Line Graphs Jay S. Bagga Department of Computer Science Ball State University, Muncie, IN 47306 USA Lowell W. Beineke Department of Mathematical Sciences Indiana University Purdue University, Fort Wayne, IN 46805-1499 USA Badri N. Varma Department of Mathematics University of Wisconsin-Fox Valley, Menasha, WI 54952 USA Abstract The super line graph of index r of a graph G has the r-sets of edges as its vertices, with two being adjacent if one has an edge that is adjacent to an edge in the other. In this paper, we continue our investigation of this graph by establishing two results, the first on the independence number of super line graphs of arbitrary index and the second on pancyclicity in the index-2 case. 1 Introduction The super line graph of index r, denoted by Lr (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. If r = 1, then this is the ordinary line graph, so the super line graph is another among the line graph generalizations that have been studied. (For a discussion of many of these, see [5]). Index-r super line graphs were introduced by the authors in [1], and we have since investigated various of their properties [2, 3]. The index-2 case has been studied in greater detail [4]. In this paper, we continue our study with two further results. The first is on the independence number of super line graphs of arbitrary index, and the second on Australasian Journal of Combinatorics 19(1999), pp.171-178