Total Face Irregularity Strength of Certain Graphs

The edge -labeling of is defined by a mapping from to a set of integers , where the integer weight assigned to the vertex is given as , such that the sum is taken over every vertex of that is adjacent to and the integer weights of adjacent vertices must be distinct for all vertices with . An irregular assignment of using atmost labels which is considered to be a minimum is defined as irregularity strength of a graph and can be denoted as . There are also further works on familiar irregular assignments, such as edge irregular labelings, vertex irregular total labelings, edge irregular total labelings, and face irregular entire -labelings of plane graphs. A plane graph can be defined as a graph that is embedded in the plane in which no two lines will be intersected. In a plane graph the number of regions present are called faces and we denote it as . The concept of total face irregularity strength is defined by the motivation of irregular networks and entire irregular face -labeling. In our paper, we have obtained a minimum bound for the total face irregularity strength of two-connected plane graphs like cycle-of-ladder, -necklace graph, -necklace graph, sibling tree, and triangular graph.