The Partition Dimension of Corona Product of Complete and Wheel Graph
Muhammad Ahnaf Yusuf, Hasmawati, Muhammad Rozzaq Hamidi, Andi Muhammad, Anwar

TL;DR
This paper investigates the partition dimension of the corona product of complete and wheel graphs, providing exact values based on the parameters n and m through mathematical analysis.
Contribution
It determines the partition dimension of the corona product of complete and wheel graphs for various parameter values, introducing new mathematical insights and methods.
Findings
For m = n, pd(K_n W_m) = n for n 03.
For m = n + 1, pd(K_n W_m) = 3 when n = 3.
For m = n + 2, pd(K_n W_m) = 4 for n = 2, 3, and pd(K_n W_m) = n for n 04.
Abstract
The graph G is a pair of sets (V(G), E(G)), where V(G) is a finite set whose elements are called vertices, and E(G) is a set of pairs of members of V(G), which is called the edges. Let G be a simple graph. For an ordered k-partition \{\Pi\} = \{S_1, S_2, \dots, S_k\} of V(G), the representation of u with respect to \{\Pi\} is k-ordered pairs, r(u \mid \{\Pi\}) = (d(u, S_1), d(u, S_2), \dots, d(u, S_k)). The partition \{\Pi\} is called a resolving partition of G if r(u \mid \{\Pi\}) \neq r(v \mid \{\Pi\}) for all distinct u, v \in V(G). The resolving partition \{\Pi\} with the minimum cardinality is called minimum resolving partition. The partition dimension of G, denoted pd(G), is the cardinality of a minimum resolving partition of G. In this research, we determine the partition dimension of the corona product of a complete graph using some mathematical statements about resolving…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Graph Theory and Algorithms · Advanced Graph Theory Research
