Double Metric Resolvability in Convex Polytopes

Abstract

Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

Monitoring edge-geodetic numbers of convex polytopes and four networks

“…We use T n to denote 3-sided, 5-sided, and n-sided faces on the convex polytope [11,12]. The T n is shown in Figure 8, and the vertex labels of T n are shown in Figure 8, we divide the vertices in the T n into three layers: the 0th, the 1st and the 2nd.…”

“…We use S n to denote 3-sided, 4-sided, and n-sided faces on the convex polytope [12][13][14], and the S n is shown in Figure 10, the vertex labels of S n are shown in Figure 10. We divide the vertices in the T n into four layers from the inside out and call them are in the 0th, the 1st, the 2nd and the 3rd layers respectively.…”

Partition Resolvability of Nanosheet and Nanotube Derived from Octagonal Grid

“…Since the partition dimension is a generalization of the metric dimension, the concepts of metric and partition dimension are closely related. We calculate the distance between a vertex and a set rather than between two vertices [25,26].…”

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

“…Nullity is expressed in terms of maximum degree of a vertex [22] , [23] . Authors of [24] , [25] , computed the double metric resolvability of convex polytopes, authors of [26] , computed the edge version of resolvability and double resolvability of some generalized graphs.…”