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On the Locating Chromatic Number of Certain Barbell Graphs

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Listed:
  • Asmiati
  • I. Ketut Sadha Gunce Yana
  • Lyra Yulianti

Abstract

The locating chromatic number of a graph is defined as the cardinality of a minimum resolving partition of the vertex set such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in are not contained in the same partition class. In this case, the coordinate of a vertex in is expressed in terms of the distances of to all partition classes. This concept is a special case of the graph partition dimension notion. In this paper we investigate the locating chromatic number for two families of barbell graphs.

Suggested Citation

  • Asmiati & I. Ketut Sadha Gunce Yana & Lyra Yulianti, 2018. "On the Locating Chromatic Number of Certain Barbell Graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-5, August.
    • Handle: RePEc:hin:jijmms:5327504
    DOI: 10.1155/2018/5327504
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    References listed on IDEAS

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    1. Varaporn Saenpholphat & Ping Zhang, 2004. "Conditional resolvability in graphs: a survey," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-21, January.
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