| dc.description.abstract | Let G be a connected graph with vertex set ( )GV and =W
{}( )....,,,
GVwww
21
m
⊂ The representation of a vertex ( ),GVv ∈
with respect to W is the ordered m-tuple ( ) ( )( ,,
() ( )),,...,,,
2 m
wvdWvr =|
wvdwvd where ( )wvd , represents the distance between vertices v and w. This set W is called a local resolving set for
G if every two adjacent vertices have a distinct representation and
a minimum local resolving set is called a local basis of G. The
cardinality of a local basis of G is called the local metric dimension of
G, denoted by
().dim G
l
In general, comb product and corona product
are non-commutative operations in graphs. However, these operations
can be made commutative with respect to local metric dimension for
some graphs with certain conditions. In this paper, we determine the
local metric dimension of generalized comb and corona products of
graphs and obtain necessary and sufficient conditions of graphs in
order that comb and corona products be commutative operations with
respect to the local metric dimension. | en_US |
