THE SIMILARITY OF METRIC DIMENSION AND LOCAL METRIC DIMENSION OF ROOTED PRODUCT GRAPH
Date
2017-09-11Author
L. Susilowati
Slamin, Slamin
M. I. Utoyo
N. Estuningsih
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Show full item recordAbstract
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.
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- LSP-Jurnal Ilmiah Dosen [7292]