| dc.description.abstract | An ordered set of vertices S is called as a (local) resolving set of a connected
graph
),(
EVG
if for any two adjacent vertices
GG
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1
Vts
have distinct representation
G
with respect to S, that is
).|()|( StrSsr
A representation of a vertex in G is a vector of
distances to vertices in S. The minimum (local) resolving set for G is called as a (local) basis of
G. A (local) metric dimension for G denoted by dim(G), is the cardinality of vertices in a basis
for G, and its local variant by dim
(G).
Given two graphs, G with vertices s
l
1
, s
2
, ..., s
p
and edges e
1
, e
2
, ..., e
, and H. An edgecorona
of
G
and
H,
GH
is
defined
as
a
graph
obtained
by
taking
a
copy
of
G
and
q
copies
of
H
and for each edge e
j
= s
i
s
h
of G joining edges between the two end-vertices s
q
and
each vertex of j-copy of H.
In this paper, we determine and compare between the metric dimension of graphs with m
pendant
points, GmK
, and its local variant for any connected graph G. We give an upper
bound of the dimensions. | en_US |
