Paper Info
Title
The Upper Forcing Geodetic Number Of A Graph
Abstract
For vertices u and v in a nontrivial connected graph G, the closed interval I[u, v] consists of u, v, and all vertices lying in some u-v geodesic of G. For S subset of or equal to V(G), the set I[S] is the union of all sets I[u, v] for u, v is an element of S. A set S of vertices of a graph G is a geodetic set in G if I[S] = V(G). The minimum cardinality of a geodetic set in G is its geodetic number g(G). A subset T of a minimum geodetic set S in a graph G is a forcing subset for S if S is the unique minimum geodetic set containing T. The forcing geodetic number f (S) of S in G is the minimum cardinality of a forcing subset for S, and the upper forcing geodetic number f(+) (G) of the graph G is the maximum forcing geodetic number among all minimum geodetic sets of G. Thus 0 less than or equal to f(+) (G) less than or equal to g (G) for every graph G. The upper forcing geodetic numbers of several classes of graphs are determined. It is shown that for every pair a, b of integers with 0 less than or equal to a less than or equal to b and b greater than or equal to 1, there exists a connected graph G with f(+)(G) = a and g (G) = b if and only if (a, b) is an element of {(1, 1), (2, 2)}.
Year
Venue
Keywords
2002
ARS COMBINATORIA
geodetic set, geodetic number, forcing geodetic number
Field
DocType
Volume
Graph,Discrete mathematics,Geodetic datum,European Combined Geodetic Network,Forcing (mathematics),Geodetic network,Geodesy,Fundamental station,Mathematics
Journal
62
ISSN
Citations 
PageRank 
0381-7032
4
0.62
References 
Authors
0
1
Name
Order
Citations
PageRank
Ping Zhang129247.70