Edge irregular reflexive labeling of prisms and wheels

For a graph <i>G</i> we define <i>k</i>-labeling <i>ρ</i> such that the edges of <i>G</i> are labeled with integers {1, 2, . . . , <i>k_e</i>} and the vertices of <i>G</i> are labeled with even integers {0, 2, . . . , 2<i>k</i>_<i>v</i>}, where <i>k</i> = max{<i>k_e</i>, 2<i>k_v</i>}. The labeling <i>ρ</i> is called an <i>edge irregular k-labeling</i> if distinct edges have distinct weights, where the edge weight is defined as the sum of the label of that edge and the labels of its ends. The smallest <i>k</i> for which such labeling exist is called the <i>reflexive edge strength</i> of <i>G</i>. In this paper we give exact values of reflexive edge strength for prisms, wheels, baskets and fans.