The total face irregularity strength of some plane graphs

• Main Authors: Meilin I. Tilukay, A.N.M. Salman, Venn Y.I. Ilwaru, F.Y. Rumlawang
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-01-01
• Series: AKCE International Journal of Graphs and Combinatorics
• Subjects: irregular total labeling; plane graph; total face irregularity strength
• Online Access: http://dx.doi.org/10.1016/j.akcej.2019.05.001

A face irregular total -labeling of a 2-connected plane graph is a labeling of vertices and edges such that their face-weights are pairwise distinct. The weight of a face under a labeling is the sum of the labels of all vertices and edges surrounding . The minimum value for which has a face irregular total -labeling is called the total face irregularity strength of , denoted by . The lower bound of 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 . We estimate the bounds of and prove that the lower bound is sharp for isomorphic to a cycle, a book with polygonal pages, or a wheel.