On minimum metric dimension of honeycomb networks

Abstract

A minimum metric basis is a minimum set W of vertices of a graph G(V , E) such that for every pair of vertices u and v of G, there exists a vertex w ∈ W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. The honeycomb and hexagonal networks are popular mesh-derived parallel architectures. Using the duality of these networks we determine minimum metric bases for hexagonal and honeycomb networks.

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

“…In light of these results, the complexity of Locating-Dominating Set and Metric Dimension for interval and permutation graphs is a natural open question (as posed in [28] and [11] for Metric Dimension on interval graphs), since these classes are standard candidates for designing ecient algorithms.…”

Computing topological indices of Sudoku graphs

“…Imran et al studied various degree based topological indices for various networks like silicates, hexagonal, honeycomb and oxide in [14]. For further study of topological indices of various graph families see, [2,9,10,12,13,15,18,[22][23][24][25]29,31,37]. …”

On Certain Connected Resolving Parameters of Hypercube Networks

“…There are many applications of resolving sets to problems of network discovery and verification [1], pattern recognition, image processing and robot navigation [2], geometrical routing protocols [10], connected joins in graphs [11] and coin weighing problems [12]. This problem has been studied for trees, multi-dimensional grids [2], Petersen graphs [13], torus networks [14], Benes networks [9], honeycomb networks [15], enhanced hypercubes [16] and Illiac networks [17].…”