THE ENTIRE FACE IRREGULARITY STRENGTH OF A BOOK WITH POLYGONAL PAGES
Meilin Imelda Tilukay, Venn Yan Ishak Ilwaru Β· BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN Β· 2015
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:πβͺπΈβͺπΉβ{1,2,β―,π} of a 2-connected plane graph πΊ=(π,πΈ,πΉ) is a labeling of vertices, edges, and faces of πΊ such that for any two different faces π and π, their weights π€π(π) and π€π(π) are distinct. The minimum π for which a plane graph πΊ has a face irregular entire π-labeling is called the entire face irregularity strength of πΊ, denoted by πππ (πΊ). This paper deals with the entire face irregularity strength of a book with π π-polygonal pages, where embedded in a plane as a closed book with πβsided external face.