Metric Dimension on Line Graph of Honeycomb Networks

Let G = (V,E) be a connected graph and distance
between any two vertices a and b in G is a−b geodesic and is denoted
by d(a, b). A set of vertices W resolves a graph G if each vertex is
uniquely determined by its vector of distances to the vertices in W.
A metric dimension of G is the minimum cardinality of a resolving
set of G. In this paper line graph of honeycomb network has been
derived and then we calculated the metric dimension on line graph
of honeycomb network.

Authors:

• M. Hussain
• Aqsa Farooq

Keywords:

• Resolving set
• metric dimension
• honeycomb network
• line graph.

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