Bounds for partition dimension of M-wheels

Abstract

Resolving partition and partition dimension have multipurpose applications in computer, networking, optimization, mastermind games and modelling of chemical substances. The problem of finding exact values of partition dimension is hard so one can find bound for the partition dimension of a general family of graph. In the present article, we give the sharp upper bounds and lower bounds for the partition dimension of m-wheel, Wn,m for all n ≥ 4 and m ≥ 1. Presented data generalise some already available results.

Double edge resolving set and exchange property for nanosheet structure

“…In materials science, octagonal grid-derived nanosheets are crucial and well-researched materials [2] , [3] , [4] . Because of their thinness, these nanostructures are valued in a variety of sectors, including nanotechnology and medicine.…”

On the Partition Dimension of Tri-Hexagonal α-Boron Nanotube

“…The graphs obtained by sum operation of cycle and path graphs are studied in [41]. [18] provided bounds of partition dimension of wheel related graphs. [15] and [27] discussed the partition dimension of circulant graph.…”

Partition Dimension of Generalized Petersen Graph

“…For example, the graph with partition dimension |V| − 3 is discussed [6] and the graph obtained by graph operations and its corresponding partition dimension is studied in [7]. e bounds on the partition dimension for convex polytopes are studied in [8][9][10] and bounds of partition on the circulant and multipartite discussed in [11,12]. e partition dimension of chemical structure fullerenes graphs is studied in [13], and on the bounded partition, dimension of the Cartesian product of graphs are studied in [14].…”