Some Types of Irregular Reflexive Labeling for the Subdivision of Wheel Graphs and Its Computation

There are two significant parameters in an irregular reflexive structure derived from total labeling, i.e., the vertex irregular reflexive labeling and the edge irregular reflexive labeling. For a graph F of order p, we construct the total l-labeling β that assigns a number from 1 to le to the edges of F and assigns a nonnegative even number from 0 to 2lv to the vertices of F. The labeling β is described as reflexive vertex (edge) irregular l-labeling if the different vertices (edges) possess different weights, where the vertex weight is determined by adding the label of the vertex to the labels of all edges that are connected to this vertex, while the weight of an edge is found by adding up the labels of its edge and the vertices that are connected to it. The least l for which these labelings exist is referred to as the reflexive-vertex strength (rvs) and reflexive-edge strength (res), respectively. In this study, the smallest number of l for these types of labelings is investigated for the subdivision of wheel graphs. More specifically, we calculate the precise amount of the reflexive vertex (edge) strength for the subdivision of wheel graphs. Moreover, we construct an algorithm to compute the weight of vertices and the precise amount of rvs of SWp.