The line graph L(G) of a graph G is defined to have as its vertices the edges of G, with two being adjacent if the corresponding edges share a vertex in G. Line graphs have a rich history. The nameâ€¦ (More)

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 areâ€¦ (More)

Biocomputational methods can broadly be viewed as information management systems at the interface of mathematics, statistics, computer science, and molecular biology/genetics. The main objective isâ€¦ (More)

The Floodlight Illumination Problem (FIP) is the determination of the minimum number of vertex-lights required to illuminate a given polygon. We show that FIP for simple polygon is NP-hard for anyâ€¦ (More)

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 degreeâ€¦ (More)

For an arbitrary simple graph G and a positive integer r, the super line multigraph of index r of G, denoted Mr(G), has for vertices all the r-subsets of edges. Two vertices S and T are joined by asâ€¦ (More)