Abstract
The concept of minimum resolving set for a connected graph has played a vital role in Robotic navigation, networking, and in computer sciences. In this article, we investigate the values of m and n for which P2⊗mPn and P2⊗mCn are connected and find metric dimension in this case. We also conclude that, for each m, we obtain a new regular family of constant metric dimension. We also give a basis for these graphs and presentation of resolving vector in general closed form with respect to the basis.
Highlights
Journal of Mathematics fan graphs, fn, and proved that, for n ≥ 7, dim(fn) ((2n + 2)/5)
Authors proved that the metric dimension of G□G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G
We like to remark that metric dimension of the tensor product of two graphs has not been extensively studied over the years
Summary
Journal of Mathematics fan graphs, fn, and proved that, for n ≥ 7, dim(fn) ((2n + 2)/5). Metric dimension of all graphs depends upon the number of vertices in the graph. Discussed some families of graphs with constant metric dimension. Another aspect is the metric dimension of a graph that is some kind of product of two other graphs.
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