Skolem Sequences and Erdosian Labellings of m Paths with 2 and 3 Vertices

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They have the property that each vertex label and edge label appears only once in the set of positive integers {c, . . . , c+ 6m− 1}. Here, we show how to construct certain c-Erdösian of m paths with 2 and 3 vertices by using Skolem sequences. Keywords—c-Erdösian, Skolem sequences, magic labelling