LAP Lambert Academic Publishing ( 2011-07-07 )
€ 59,00
In this work, we deal with three types of distances, namely ordinary distance, the minimum distance (n-distance), and the width distance (w-distance). The ordinary distance between two distinct vertices u and v in a connected graph G is defined as the minimum of the lengths of all u-v paths in G, and usually denoted by dG(u,v), or d(u,v).The minimum distance in a connected graph G between a singleton vertex v belong to V and (n-1)-subset S of V , n ≥ 2, denoted by dn(u,v) and termed n-distance, is the minimum of the distances from v to the vertices in S.The container between two distinct vertices u and v in a connected graph G is defined as a set of vertex-disjoint u-v paths, and is denoted by C(u,v). The container width w = w(C(u,v)) , is the number of paths in the container, i.e.,w(C(u,v)) = |C(u.v)|. The length of a container l = l(C(u,v)) is the length of a longest path in C(u,v).For every fixed positive integer w, the width distance (w-distance) between u and v is defined as: dn* (u,v|G)= min l(C(u,v)) ,where the minimum is taken over all containers C(u,v) of width w. Assume that the vertices u and v are distinct when w ≥ 2.
Book Details: |
|
ISBN-13: |
978-3-8454-0101-0 |
ISBN-10: |
384540101X |
EAN: |
9783845401010 |
Book language: |
English |
By (author) : |
Ahmed M. Ali |
Number of pages: |
148 |
Published on: |
2011-07-07 |
Category: |
Mathematics |