Harmonious Graph

A connected Labeled Graph with Edges in which all Vertices can belabeled with distinct Integers (mod ) so that the sums of the Pairs of numbers at theends of each Edge are also distinct (mod ). The Ladder Graph, Fan, WheelGraph, Petersen Graph, Tetrahedral Graph, Dodecahedral Graph, and IcosahedralGraph are all harmonious (Graham and Sloane 1980).

References

Gallian, J. A. ``Open Problems in Grid Labeling.'' Amer. Math. Monthly 97, 133-135, 1990.

Gardner, M. Wheels, Life, and other Mathematical Amusements. New York: W. H. Freeman, p. 164, 1983.

Graham, R. L. and Sloane, N. ``On Additive Bases and Harmonious Graphs.'' SIAM J. Algebraic Discrete Math. 1, 382-404, 1980.

Guy, R. K. ``The Corresponding Modular Covering Problem. Harmonious Labelling of Graphs.'' §C13 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 127-128, 1994.

• Continued Fraction Map
• Continued Fraction Unit Fraction Algorithm
• Continued Square Root
• Continued Vector Product
• Continuity
• Continuity Axioms
• Continuity Correction
• Continuity Principle
• Continuous
• Continuous Distribution
• Continuous Function
• Continuous Space
• Continuum
• Continuum Hypothesis
• Contour
• Contour Integral
• Contour Integration
• Contracted Cycloid
• Contraction
• Contraction (Graph)
• Contraction (Tensor)
• Contradiction Law
• Contravariant Tensor
• Contravariant Vector
• Control Theory