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.

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U2 - 10.1155/2020/4197678

DO - 10.1155/2020/4197678

M3 - Article

AN - SCOPUS:85092535964

VL - 2020

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

SN - 1026-0226

M1 - 4197678

ER -