Computing dominant metric dimensions of certain connected networks

Abstract

In the studies of the connected networks, metric dimension being a distance-based parameter got much more attention of the researches due to its wide range of applications in different areas of chemistry and computer science. At present its various types such as local metric dimension, mixed metric dimension, solid metric dimension, and dominant metric dimension have been used to solve the problems related to drug discoveries, embedding of biological sequence data, classification of chemical compounds, linear optimization, robot navigation, differentiating the interconnected networks, detecting network motifs, image processing, source localization and sensor networking. Dominant resolving sets are better than resolving sets because they carry the property of domination. In this paper, we obtain the dominant metric dimension of wheel, gear and anti-web wheel network in the form of integral numbers. We observe that the aforesaid networks have bounded dominant metric dimension as the order of the network increases. In particular, we also discuss the importance of the obtained results for the robot navigation networking.

Keywords

• Metric dimension
• Dominant metric dimension
• Connected networks