Jay Bagga

JGraph— A Java Based System for Drawing Graphs and Running Graph Algorithms

The JGraph system has been used as a learning tool. A version of this system is available on the web (http://www.cs.bsu.edu/homepages/gnet.) This is an ongoing project. New features and algorithms will continue to be added. Suggestions and comments are greatly welcome. The first author can be contacted at jbagga@bsu.edu.

THE SUPER LINE GRAPH L2

Abstract In Bagga et al. (1995) the authors introduced the concept of the super line graph of index r of a graph G, denoted by L r (G) . The vertices of L r (G) are the r-subsets of E ( G ) and two vertices S and T are adjacent if there exist s ∈ S and t ∈ T such that s and t are adjacent edges in G. In this paper, some properties of super line graphs of index 2 are presented, and L 2 (G) is studied for certain classes of graphs.

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 S/sub k/(G) which has for vertices all the k-subsets of E(G), and two vertices S and T are adjacent whenever there exist sϵS and tϵT such that s and t share a common vertex. In the super line multigraph L/sub k/(G) we have an adjacency for each such occurrence. We give a formula to find the adjacency matrix of L/sub k/(G). If G is a regular graph, we calculate all the eigenvalues of L/sub k/(G) and their multiplicities. From those results we give an upper bound on the number of isolated vertices.

Theoretical Computer Science and Discrete Mathematics

A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of G. The degree associated reconstruction number of a graph G (or drn(G)) is the size of the smallest collection of dacards of G that uniquely determines G. It is shown that drn(G) = 1 or 2 for all biregular bipartite graphs with degrees d and d+ k, k ≥ 2 except the bistar B2,2 on 6 vertices and that drn(B2,2) = 3.

New Classes of Graceful Unicyclic Graphs

Abstract A C n -unicyclic graph is a unicyclic graph where the cycle has n ≥ 3 vertices. A caterpillar R with spine P n = v 0 v 1 ⋯ v n − 1 is denoted by R ( v 0 v 1 ⋯ v n − 1 ) . A cycle with a pendant caterpillar is obtained by identifying a vertex of the cycle with a leaf of R ( v 0 v 1 ⋯ v n − 1 ) that is adjacent to v 0 (or v n − 1 ). In this paper, we investigate the gracefulness of unicyclic graphs with pendant caterpillars at two adjacent vertices of the cycle, and pendant edges at some other vertices of the cycle.

Illuminating simple polygons by floodlights

We consider the problem of illuminating a simple polygon by flood-lights. We show that the problem of placing the minimum number of 90 degree(s) flood-lights to illuminate the interior of a polygon is NP-hard.