| dc.description.abstract | Let G be a connected graph with vertex set ( )GV and =W
{}()....,,,
⊂ The representation of a vertex ( )GVv ∈ with
respect to W is the ordered k-tuple
( ) ( ) ( )( ...,,,,,
GVwww
21
()),,
k
k
1
wvdwvdWvr =|
21
wvd where ()wvd , represents the distance between vertices v
and w. The set W is called a resolving set for G if every vertex of G
has a distinct representation. A resolving set containing a minimum number of vertices is called basis for G. The metric dimension of G,
denoted by
(),dim G is the number of vertices in a basis of G. If every
two adjacent vertices of G have a distinct representation with respect
to W, then the set W is called a local resolving set for G and the
minimum local resolving set is called a local basis of G. The
cardinality of a local basis of G is called local metric dimension
of G, denoted by
( ).dim G
l
In this paper, we study the local metric
dimension of rooted product graph and the similarity of metric
dimension and local metric dimension of rooted product graph. | en_US |
