Proceedings - Mathematical Sciences

, Volume 127, Issue 5, pp 755–767 | Cite as

On the partition dimension of two-component graphs

  • D O HaryeniEmail author
  • E T Baskoro
  • S W Saputro
  • M Bača
  • A Semaničová-Feňovčíková


In this paper, we continue investigating the partition dimension for disconnected graphs. We determine the partition dimension for some classes of disconnected graphs G consisting of two components. If \(G=G_1 \cup G_2\), then we give the bounds of the partition dimension of G for \(G_1 = P_n\) or \(G_1=C_n\) and also for \(pd(G_1)=pd(G_2)\).


Partition dimension disconnected graph component 

2010 Mathematics Subject Classification

05C12 05C15 



This research was supported by Research Grant: “Program Penelitian dan Pengabdian kepada Masyarakat-Institut Teknologi Bandung (P3MI-ITB)”, Ministry of Research, Technology and Higher Education, Indonesia. The research for this article was also supported by APVV-15-0116 and by VEGA 1/0233/18.


  1. 1.
    Baskoro E T and Darmaji, The partition dimension of corona product of two graphs, Far East J. Math. Sci. 66 (2012) 181–196Google Scholar
  2. 2.
    Chartrand G, Salehi E and Zhang P, On the partition dimension of a graph, Congr. Numer. 131 (1998) 55–66MathSciNetzbMATHGoogle Scholar
  3. 3.
    Chartrand G, Salehi E and Zhang P, The partition dimension of a graph, Aequ. Math. 59 (2000) 45–54MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Darmaji, Baskoro E T, Utunggadewa S and Simanjuntak R, The partition dimension of complete multipartite graph, a special caterpillar and a windmill, J. Combin. Math. Combin. Comput. 71 (2009) 209–215Google Scholar
  5. 5.
    Grigorious C, Stephen S, Rajan B and Miller M, On partition dimension of a class of circulant graphs, Inf. Process. Lett. 114 (2014) 353–356MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Haryeni D O, Baskoro E T and Saputro S W, Partition dimension of disconnected graphs. J. Math. Fund. Sci. 49 (2017) 18–32Google Scholar
  7. 7.
    Haryeni D O and Baskoro E T, Partition dimension of some classes of homogeneous disconnected graphs, Proc. Comput. Sci. 74 (2015) 73–78CrossRefGoogle Scholar
  8. 8.
    Rodríguez-Velázquez J A, Yero I G and Kuziak D, The partition dimension of corona product graphs, Ars Combin. 127 (2016) 387–399Google Scholar
  9. 9.
    Rodríguez-Velázquez J A, Yero I G and Lemańska M, On the partition dimension of trees, Discrete Appl. Math. 166 (2014) 204–209MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tomescu I, Discrepancies between metric dimension and partition dimension of a connected graph, Discrete Math. 308 (2008) 5026–5031MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Yero I G, Kuziak D and Rodríguez-Velázquez J A, A note on the partition dimension of Cartesian product graphs, Appl. Math. Comput. 217 (2010) 3571–3574MathSciNetzbMATHGoogle Scholar
  12. 12.
    Yero I G, Jakovac M, Kuziak D and Taranenko A, The partition dimension of strong product graphs and Cartesian product graphs, Discrete Math. 331 (2014) 43–52MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  • D O Haryeni
    • 1
    Email author
  • E T Baskoro
    • 1
  • S W Saputro
    • 1
  • M Bača
    • 2
  • A Semaničová-Feňovčíková
    • 2
  1. 1.Combinatorial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural SciencesInstitut Teknologi Bandung (ITB)BandungIndonesia
  2. 2.Department of Applied Mathematics and InformaticsTechnical UniversityKosiceSlovak Republic

Personalised recommendations