On The Partition Dimension of Disconnected Graphs | Zendy

Debi Oktia Haryeni | Zendy; Edy Tri Baskoro | Zendy; Suhadi Wido Saputro | Zendy

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On The Partition Dimension of Disconnected Graphs

Author(s) -

Debi Oktia Haryeni,

Edy Tri Baskoro,

Suhadi Wido Saputro

Publication year - 2017

Publication title -

journal of mathematical and fundamental sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.216

H-Index - 12

eISSN - 2337-5760

pISSN - 2338-5510

DOI - 10.5614/j.math.fund.sci.2017.49.1.2

Subject(s) - mathematics , partition (number theory) , combinatorics , frequency partition of a graph , metric dimension , vertex (graph theory) , graph partition , discrete mathematics , graph , dimension (graph theory) , chordal graph , line graph , 1 planar graph , graph power

For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω. The partition dimension of G is the minimum integer k such that G has a resolving k-partition. Many results in determining the partition dimension of graphs have been obtained. However, the known results are limited to connected graphs. In this study, the notion of the partition dimension of a graph is extended so that it can be applied to disconnected graphs as well. Some lower and upper bounds for the partition dimension of a disconnected graph are determined (if they are finite). In this paper, also the partition dimensions for some classes of disconnected graphs are given

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