Distance-Based Fractional Dimension of Certain Wheel Networks

Abstract

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 RLuv is a set of vertices of W which resolve uv. A mapping α:VW⟶0,1 is called local resolving function of W if αRLuv≥1 for any adjacent pair of vertices of uv of W and the minimal value of αRLuv 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.