The total face irregularity strength of some plane graphs
Meilin Imelda Tilukay, A.N.M. Salman, Venn Yan Ishak Ilwaru, Francis Yunito Rumlawang Β· AKCE International Journal of Graphs and Combinatorics Β· 2019
A face irregular total π-labeling π:πβͺπΈβ{1,2,β¦,π} of a 2-connected plane graph πΊ is a labeling of vertices and edges such that their face-weights are pairwise distinct. The weight of a face π under a labeling π is the sum of the labels of all vertices and edges surrounding π. The minimum value π for which πΊ has a face irregular total π-labeling is called the total face irregularity strength of πΊ, denoted by π‘β’πβ’π β‘(πΊ). The lower bound of π‘β’πβ’π β‘(πΊ) is provided along with the exact value of two certain plane graphs. Improving the results, this paper deals with the total face irregularity strength of the disjoint union of multiple copies of a plane graph πΊ. We estimate the bounds of π‘β’πβ’π β‘(πΊ) and prove that the lower bound is sharp for πΊ isomorphic to a cycle, a book with π polygonal pages, or a wheel.