Putting the concept of line graph in a more general setting, for a positive integer k the k-line graph Lk(G) of a graph G has the Kk-subgraphs of G as its vertices, and two vertices of Lk(G) are adjacent if the corresponding copies of Kk in G share k− 1 vertices. Then, 2-line graph is just the line graph in usual sense, whilst 3-line graph is also known as triangle graph. The k-anti-Gallai grap...

Graphoto is a framework that automatically generates a photo or adjusts an existing one to match a line graph. Since aesthetics is an important element in visualizing personal data, Graphoto provides users with aesthetically pleasing displays for casual line graph information visualization. More specifically, after creating a line graph of the input data, a photo that resembles the input data o...

We present a dynamic data structure for the incremental construction of a planar embedding of a planar graph. The data structure supports the following Ž . operations: i testing if a new edge can be added to the embedding without Ž . introducing crossing; and ii adding vertices and edges. The time complexity of Ž . Ž . each operation is O log n amortized for edge insertion , and the memory spac...

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.