There are various representations for encoding graph structures, such as artificial neural networks (ANNs) and circuits, each with its own strengths and weaknesses. Here we analyz...
A hub set in a graph G is a set U V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G) hc(G) c(G) h(G) + 1, ...
Tracy Grauman, Stephen G. Hartke, Adam Jobson, Bil...
Consider a planar straight line graph (PSLG), G, with k connected components, k 2. We show that if no component is a singleton, we can always find a vertex in one component that s...
Ferran Hurtado, Mikio Kano, David Rappaport, Csaba...
We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property π is called a π-graph. If π satis...
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph ...