Theory and Applications of Graphs pp 394-402 | Cite as

# Steinhaus graphs

## 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

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