A polynema of order is Kyrmse's term for a connected graph having edges. An -polynema must therefore have either or nodes. The numbers of -polynemas for , 3 ... are 1, 1, 3, 5, 12, 30, 79, 227, ... (Sloane's A002905). Polynemas are related to a graphical construction problem called the match problem (Gardner 1991).

Gardner, M. "The Problem of the Six Matches." In The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, pp. 79-81, 1991.

Kyrmse, R. http://www.geocities.com/kyrmse/POLIN-E.htm.

Sloane, N. J. A. Sequence A002905/M2486 in "The On-Line Encyclopedia of Integer Sequences."

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Weisstein, Eric W. "Polynema." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Polynema.html