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Steinhaus graphs

  • John C. Molluzzo
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 642)

Abstract

A Steinhaus triangle is formed by starting with an arbitrary row of plus and minus signs. Each succeeding row is formed by placing a plus or minus sign under each pair of equal or opposite signs respectively. A Steinhaus graph is constructed by considering this triangle as the upper triangle of an adjacency matrix. The minimum number of lines possible in a Steinhaus graph is found and a theorem is obtained on the structure of these minimal graphs. Methods of constructing digraphs and valued graphs from Steinhaus triangles are discussed. Problems on the several types of graph are posed. Finally, a generalization of Steinhaus' original problem is made.

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References

  1. 1.
    F. Harary, Graph Theory, Addison-Wesley, Reading, Mass. (1969).Google Scholar
  2. 2.
    F. Harary, R.Z. Norman, and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs, John Wiley and Sons, New York (1965).MATHGoogle Scholar
  3. 3.
    H. Harborth, Solution of Steinhaus's Problem with Plus and Minus Signs, J. Combinatorial Theory, Ser. A,12 (1972)Google Scholar
  4. 4.
    H. Steinhaus, One Hundred Problems in Elementary Mathematics, Pergamon, Elinsford, N.Y. (1963).MATHGoogle Scholar
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    E. Wang, Problem E2541, Amer. Math. Monthly 82 (1975) 659–660.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • John C. Molluzzo
    • 1
  1. 1.St. John's UniversityStaten IslandUSA

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