Local Fractional Metric Dimensions of Rotationally Symmetric and Planar Networks

Abstract

Mathematical modeling, coding or labeling with the help of numeric numbers based on the parameter of distance plays a vital role in the studies of the structural properties of the networks such as accessibility, centrality, clustering, complexity, connectivity, modularity, robustness and vulnerability. In particular, various distance based dimensions of the networks are used to rectify the problems in different strata of computer science and chemistry such as navigation, image processing, pattern recognition, integer programming problem, drug discovery and formation of different chemical compounds. In this note, we consider a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangles, quadrangles and pentagons. We compute local fractional metric dimensions of the aforesaid networks and study their boundedness. Moreover, our findings at the closure of this note have been summarized in the form of tables and 3-D plots.