TY - JOUR
T1 - Resolvability in Subdivision of Circulant Networks Cn1,k
AU - Wei, Jianxin
AU - Bokhary, Syed Ahtsham Ul Haq
AU - Abbas, Ghulam
AU - Imran, Muhammad
N1 - Publisher Copyright:
© 2020 Jianxin Wei et al.
PY - 2020
Y1 - 2020
N2 - Circulant networks form a very important and widely explored class of graphs due to their interesting and wide-range applications in networking, facility location problems, and their symmetric properties. A resolving set is a subset of vertices of a connected graph such that each vertex of the graph is determined uniquely by its distances to that set. A resolving set of the graph that has the minimum cardinality is called the basis of the graph, and the number of elements in the basis is called the metric dimension of the graph. In this paper, the metric dimension is computed for the graph Gn1,k constructed from the circulant graph Cn1,k by subdividing its edges. We have shown that, for k=2, Gn1,k has an unbounded metric dimension, and for k=3 and 4, Gn1,k has a bounded metric dimension.
AB - Circulant networks form a very important and widely explored class of graphs due to their interesting and wide-range applications in networking, facility location problems, and their symmetric properties. A resolving set is a subset of vertices of a connected graph such that each vertex of the graph is determined uniquely by its distances to that set. A resolving set of the graph that has the minimum cardinality is called the basis of the graph, and the number of elements in the basis is called the metric dimension of the graph. In this paper, the metric dimension is computed for the graph Gn1,k constructed from the circulant graph Cn1,k by subdividing its edges. We have shown that, for k=2, Gn1,k has an unbounded metric dimension, and for k=3 and 4, Gn1,k has a bounded metric dimension.
UR - http://www.scopus.com/inward/record.url?scp=85092535964&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85092535964&partnerID=8YFLogxK
U2 - 10.1155/2020/4197678
DO - 10.1155/2020/4197678
M3 - Article
AN - SCOPUS:85092535964
SN - 1026-0226
VL - 2020
JO - Discrete Dynamics in Nature and Society
JF - Discrete Dynamics in Nature and Society
M1 - 4197678
ER -