Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Abstract

In this study, we used grids and wheel graphs G=V,E,F, which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k-labeling of type α,β,γ. In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k-labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfsG. We also discussed a special case of total face irregularity strength of plane graphs under k-labeling of type (1, 1, 0). The results will be verified by using figures and examples.