Vertex irregular reflexive labeling of prisms and wheels
Dushyant Tanna, Joe Ryan, Andrea Semaničová–Feňovčíková, Martin Bača · AKCE International Journal of Graphs and Combinatorics · 2018
For a graph G we define k-labeling ρ such that the edges of G are labeled with integers {1,2,…,ke} and the vertices of G are labeled with even integers {0,2,…,2kv}, where k=max{ke,2kv}. The labeling ρ is called a vertex irregular reflexive k-labeling if distinct vertices have distinct weights, where the vertex weight is defined as the sum of the label of that vertex and the labels of all edges incident this vertex. The smallest k for which such labeling exists is called the reflexive vertex strength of G.In this paper, we give exact values of reflexive vertex strength for prisms, wheels, fan graphs and baskets.