1. ABDUL ALEEM MUGHAL - Department of Mathematics, University of Management and Technology, Lahore, Pakistan.

2. RAJA NOSHAD JAMIL - Department of Mathematics, University of Management and Technology, Lahore, Pakistan.

3. ABAID UR REHMAN VIRK - Department of Mathematics, University of Management and Technology, Lahore, Pakistan.

4. MURAT CANCAN - Faculty of Education, Yuzuncu Yil University, Van, Turkey.

Wheel graphs can be constructed by adding an additional vertex on the center of a cycle graph and then joining this vertex with all other surrounding vertices. A 𝑘 −labeling of type (𝛼, 𝛽, 𝛾) in a wheel graph is a labeling from graph elements into the set of positive integers. Face irregularity strength of a wheel graph 𝑊𝑛 with respect to 𝑘 −labeling of type (𝛼, 𝛽, 𝛾) is the minimum integer 𝑘 on which the face weights of the graph are distinct. We investigate the exact value for the face irregularity strength with respect to vertex 𝑘 −labeling, edge 𝑘 −labeling and total 𝑘 −labeling of wheel graphs. Some real life applications on face irregularity strength of graphs are discovered and their models are discussed which will be helpful in practical situations.

Wheel graphs, Face irregularity strength, Applications of irregularity strength of graphs.