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Vertex irregular reflexive labeling of prisms and wheels

Abstract:

For a graph (Formula presented.) we define (Formula presented.) -labeling (Formula presented.) such that the edges of (Formula presented.) are labeled with integers (Formula presented.) and the vertices of (Formula presented.) are labeled with even integers (Formula presented.), where (Formula presented.). The labeling (Formula presented.) is called a vertex irregular reflexive (Formula presented.) -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 (Formula presented.) for which such labeling exists is called the reflexive vertex strength of (Formula presented.). In this paper, we give exact values of reflexive vertex strength for prisms, wheels, fan graphs and baskets.