Isnaini Rosyida, Diana Ayu Lestari, Wakhid Fitri Albar, Diari Indriati
A function "φ:V∩E→{1,2,⋯k}"on a 2-"connected plane graph"G = (V, E, F) is mentioned as a "face irregular total-k labeling"of G if the face-weights are all different. The weight of a face f, denoted as wφ (f), is the total amount of the labels of vertices and edges that confine f. "The total face irregularity strength (tfs)"of G is the smallest positive number k so that a "face irregular total k-labeling"of G exists. This labeling could be used to model real problems, such as a communication network model between companies. Therefore, we are interested to calculate the tfs of the "comb product"of path and cycle graphs Pn ▹ Ck and obtain the optimum label so that the t f s(Pn ▹ Ck) =[2k+n-1]/2k for n≥2,k≥3. © 2025 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang, Central Java, Semarang, 50229, Indonesia; Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Central Java, Surakarta, 57126, Indonesia
