Pre-Topology Generated by the Short Path Problems
: Graph theory
Short path problem
Closure operators
j-pre-topology
j
= 1
2
j-dependency
j = 1
2.
Restriction
Separators
Rate of liaison.
Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric