To cement the question, consider a simple example: a graph with three connected vertices in the shape of a triangle. You can isolate any two vertices and see that they share an odd number of ...

The Graphalytics benchmark is an industrial-grade benchmark for graph analysis. This benchmark can test datasets with up to 100 million vertices and 9.4 billion edges.

L (p,1)-labeling: A specific graph labelling formulation where adjacent vertices receive labels differing by at least p and vertices at distance two receive labels differing by at least one, used ...

Now to define our problem more exactly. The line graph of the complete bipartite graph on sets with m and n vertices, denoted by L (Bmn), is the graph with mn vertices given by all ordered pairs (i, j ...

Consider a graph on randomly scattered points in an arbitrary space, with any two points x, y connected with probability ϕ (x, y). Suppose the number of points is large but the mean number of isolated ...