The partition dimension of the vertex amalgamation of some cycles


Hasmawati, - and Nurdin Hinding, - and Budi Nurwahyu, - and Ahmad Syukur Daming, - and Amir Kamal Amir, - The partition dimension of the vertex amalgamation of some cycles. Heliyon Volume 8, Issue 6, June 2022.

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Abstract (Abstrak)

Let G=(V(G),E(G)) be a connected, finite, simple, and undirected graph. The distance between two vertices u,w∈V(G), denoted by d(u,w), is the shortest length of (u,w)-path in G. The distance between a vertex v∈V(G) is defined as min⁡{d(v,x):x∈S} where S⊂V(G), denoted by d(v,S). For an ordered partition Π={S1,S2,…,Sk} of the vertices of a graph G, the partition representation of a vertex v∈V(G) with respect to Π is defined as the k-vektor r(v|Π)=(d(v,S1),d(v,S1),…,d(v,S1). The partition set Π is called a resolving partition of G, if r(u|Π)≠r(v|Π), for all u≠v, u,v∈V(G). The partition dimension of G is the minimum number of sets in any resolving partition of G. In this paper we study the partition dimension of the vertex amalgamation of some cycles. Specifically, we present the vertex amalgamation of m copies of the cycle Cn at a fixed vertex v∈V(Cn), for n≥6 and k2−3k+42≤m≤k2−k2, k≥3.

Item Type: Article
Subjects: Q Science > Q Science (General)
Depositing User: - Andi Anna
Date Deposited: 15 Jun 2022 05:37
Last Modified: 15 Jun 2022 05:37
URI: http://repository.unhas.ac.id:443/id/eprint/16923

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