On graph coloring check-digit method

Abstract

We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the result is outlined. Next, graph coloring based check-digit scheme is proposed. We use quantitative result derived, to show, that feasibility of the proposed scheme increases with size of the number which digits are checked, and overall probability of digits errors.

7 pages, paper sumitted to Applied Mathematics Letters (Elsevier)

Cited by in corpus (2)

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• The upper bound on number of graphs, with fixed number of vertices, that vertices can be colored with n colors