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 π’Œ-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 πœ†:𝑉βˆͺ𝐸βˆͺ𝐹→{1,2,β‹―,π‘˜} of a 2-connected plane graph 𝐺=(𝑉,𝐸,𝐹) is a labeling of vertices, edges, and faces of 𝐺 such that for any two different faces 𝑓 and 𝑔, their weights π‘€πœ†(𝑓) and π‘€πœ†(𝑓) are distinct. The minimum π‘˜ for which a plane graph 𝐺 has a face irregular entire π‘˜-labeling is called the entire face irregularity strength of 𝐺, denoted by 𝑒𝑓𝑠(𝐺). This paper deals with the entire face irregularity strength of a book with π‘š 𝑛-polygonal pages, where embedded in a plane as a closed book with π‘›βˆ’sided external face.

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References

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Published
2018-02-01
How to Cite
[1]
M. Tilukay and V. Ilwaru, β€œTHE ENTIRE FACE IRREGULARITY STRENGTH OF A BOOK WITH POLYGONAL PAGES”, BAREKENG, vol. 9, no. 2, pp. 103-108, Feb. 2018.