Pre-Topology Generated by the Short Path Problems

M. Shokry; Y. Y. Yousif

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Publication Date

Sun Jan 01 2012

Journal Name

International Journal Of Contemporary Mathematical Sciences

Volume

7

Issue Number

17

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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.

M. Shokry

Y. Y. Yousif

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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

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