Distance-Based Fractional Dimension of Certain Wheel Networks

Metric dimension is one of the distance-based parameters which are used to find the position of the robot in a network space by utilizing lesser number of notes and minimum consumption of time. It is also used to characterize the chemical compounds. The metric dimension has a wide range of applications in the field of computer science such as integer programming, radar tracking, pattern recognition, robot navigation, and image processing. A vertex x in a network W resolves the adjacent pair of vertices uv if x attains an unequal distance from end points of uv . A local resolving neighbourhood set RL<mfenced open="(" close=")" separators="|">uv</mfenced> is a set of vertices of W which resolve uv . A mapping α:V<mfenced open="(" close=")" separators="|">W</mfenced>⟶<mfenced open="[" close="]" separators="|">0,1</mfenced> is called local resolving function of W if α<mfenced open="(" close=")" separators="|">RL<mfenced open="(" close=")" separators="|">uv</mfenced></mfenced>≥1 for any adjacent pair of vertices of uv of W and the minimal value of α<mfenced open="(" close=")" separators="|">RL<mfenced open="(" close=")" separators="|">uv</mfenced></mfenced> for all local resolving functions α of W is called local fractional metric dimension of W . In this paper, we have studied the local fractional metric dimension of wheel-related networks such as web-wheel network, subdivision of wheel network, line network of subdivision of wheel network, and double-wheel network and also examined their boundedness.