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

Authors: H. V. Chen

Abstract:

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070203

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References:


[1] J. Abrham and A. Kotzig, Skolem sequences and additive permutations, Discrete Math. 37 (1981) 143-146.
[2] C. Baker, Extended Skolem sequences, J. Combin. Des. 3 (1995), 363- 379.
[3] H. V. Chen, A Total Labellings of m Triangles, submitted.
[4] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull., 13 (1970) 451-461.
[5] J. A. MacDougall, M. Miller, Slamin, and W. D. Wallis, Vertex-magic total labellings of graphs, Util. Math. 61 (2002) 3-21.
[6] E. S. O-Keefe, Verification of a conjecture of Th Skolem, Math. Scand. 9 (1961) 80-82.
[7] J. Sedl'aˇcek, Problem 27, in Theory of Graphs and its Applications, Proc. Symposium Smolenice, June, (1963) 163-167.
[8] J. E. Simpson, Langford sequences: perfect and hooked, Discrete Math. 44 (1983) 97-104.
[9] Th. Skolem, On certain distributions of integers in pairs with given difference, Math. Scand. 5 (1957) 57-68.