The locating number of hexagonal Möbius ladder network

Abstract

Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called locating/resolving set. Minimum number of nodes in the locating set is called locating number. In this article, we find the exact value of locating number of newly designed hexagonal Möbius ladder network.

On the Edge Metric Dimension of Different Families of Möbius Networks

“…is graph contains ψ-horizontal cycles of order six. e metric dimension of the hexagonal Möbius ladder network is three [25]. In this section, we proved that edge metric dimension is also three for the hexagonal Möbius ladder network.…”

“…Hexagonal Möbius ladder HML ψ is built in [25], it can be constructed by dividing each horizontal edge of a square grid by inserting a new vertex, it becomes a grid of ψ × 1 with each cycle having order six, and now, twist this grid at 180 ∘ and paste the extreme most left and right paths of vertices as shown in Figure 2. is graph contains ψ-horizontal cycles of order six.…”

Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid

“…As we discussed above that this has numerous use in the chemical field, much work has done with graph prospectives and metric dimension also consider important to study different structures with it, like the structure of H-Naphtalenic and V C 5 C 7 nano-tubes discussed with metric concept [20], some upper bounds of cellulose network considering metric dimension as a point of discussion [43], metric of silicate star are computed in [44], a two-dimensional lattice of αboron nanotubes discussed with specific applications in terms of metric dimension in [19]. For the partition dimension, a graph with n − 3, partition dimension discussed in [3], (4, 6) is a special type of fullerene structure and it is also studied by [29] with the concept of partition dimension, There are few very recent research on the bounded partition dimension, we encourage to have a look the articles [10], [27], [31]. The bounds of partitioning on the specific type of nanotube are studied in [39].…”

Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

“…The results regarding the metric dimensions of path, cycle, Petersen, generalized Petersen networks and generalized Petersen multigraphs can be seen in [9][10][11][12][13]. Similarly, the results for the partition dimensions of convex polytopes and a hexagonal Möbius Ladder have been found in [14][15][16]. Moreover, the metric dimension was used by Chartrand et al to solve the integer programming problem (IPP) [12].…”