Improved Lower Bound of LFMD with Applications of Prism-Related Networks

Abstract

The different distance-based parameters are used to study the problems in various fields of computer science and chemistry such as pattern recognition, image processing, integer programming, navigation, drug discovery, and formation of different chemical compounds. In particular, distance among the nodes (vertices) of the networks plays a supreme role to study structural properties of networks such as connectivity, robustness, completeness, complexity, and clustering. Metric dimension is used to find the locations of machines with respect to minimum utilization of time, lesser number of the utilized nodes as places of the objects, and shortest distance among destinations. In this paper, lower bound of local fractional metric dimension for the connected networks is improved from unity and expressed in terms of ratio obtained by the cardinalities of the under-study network and the local resolving neighbourhood with maximum order for some edges of network. In the same context, the LFMDs of prism-related networks such as circular diagonal ladder, antiprism, triangular winged prism, and sun flower networks are computed with the help of obtained criteria. At the end, the bounded- and unboundedness of the obtained results is also shown numerically.

Study of Convexo-Symmetric Networks via Fractional Dimensions

“…We close this section by presenting 2 important results that will be required to prove our findings. We are presenting here their precise points in the proofs, for their details reader may see [14] and [15].…”

“…Similarly, one can find results regarding the LFMD of circular networks in, [11]. In the same manner, one can find the general criteria for the interval of LFMD for all the connected networks in [14] and improved lower bound criteria in [15]. In this paper, the family of networks (convex polytopes) is chosen that bears the symmetry with respect to rotation.…”

Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions

“…Ali et al [35] studied the properties of faulttolerant resolving sets and fault-tolerant metric dimension of hollow coronoid HC(p, q, s). Javaid et al [36] studied the properties of local fractional metric dimension of Prism related networks. Javaid et al [37] studied the properties of sharp bounds of local fractional metric dimension of wheel related networks.…”

Local Fractional Locating Number of Convex Polytope Networks

“…Javaid et al developed sharp bounds of LFLN of all the connected networks and they computed upped bounds of local FLN of wheel-related networks. Furthermore, they also improved the lower bound of LFLN di erent from unity and also developed a technique to compute exact value of LFLN under speci c conditions [35,36]. For the study of LFLN of generalized gear, sunlet and convex polytope networks see [37][38][39].…”