THE ENTIRE FACE IRREGULARITY STRENGTH OF A BOOK WITH POLYGONAL PAGES

  • Meilin I. Tilukay Jurusan Matematika FMIPA Universitas Pattimura
  • Venn Y. I. Ilwaru Jurusan Matematika FMIPA Universitas Pattimura
Keywords: Book, entire face irregularity strength, face irregular entire 𝒌-labeling, plane graph, polygonal page.

Abstract

A face irregular entire labeling is introduced by Baca et al. recently, as a modification of the well-known vertex irregular and edge irregular total labeling of graphs and the idea of the entire colouring of plane graph. A face irregular entire k-labeling ðœ†:ð‘‰âˆªð¸âˆªð¹â†’{1,2,⋯,ð‘˜} of a 2-connected plane graph ðº=(ð‘‰,ð¸,ð¹) is a labeling of vertices, edges, and faces of ðº such that for any two different faces ð‘“ and ð‘”, their weights ð‘¤ðœ†(ð‘“) and ð‘¤ðœ†(ð‘“) are distinct. The minimum 𑘠for which a plane graph ðº has a face irregular entire ð‘˜-labeling is called the entire face irregularity strength of ðº, denoted by ð‘’ð‘“ð‘ (ðº). This paper deals with the entire face irregularity strength of a book with ð‘š ð‘›-polygonal pages, where embedded in a plane as a closed book with ð‘›âˆ’sided external face.

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References

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Published
2015-12-01
How to Cite
[1]
M. Tilukay and V. Ilwaru, “THE ENTIRE FACE IRREGULARITY STRENGTH OF A BOOK WITH POLYGONAL PAGES”, BAREKENG: J. Il. Mat. & Ter., vol. 9, no. 2, pp. 103-108, Dec. 2015.