There appears to be no standard term for a simple connected graph with exactly n edges, though the words "polynema" (Kyrmse) and "polyedge" (Muñiz 2011) have been proposed. The numbers of n-polynemas for n=2, 3 ... are 1, 1, 3, 5, 12, 30, 79, 227, ... (OEIS A002905).

An n-polynema has n+1-gamma nodes, where gamma is its circuit rank.

Polynemas are related to a graphical construction problem called the match problem (Gardner 1991).

See also

Connected Graph, Match Problem, Planar Connected Graph, Polyedge, Tree

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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. "Polynemas."ñiz, A. "Puzzle Zapper Blog: Pentaedges." Apr. 10, 2011.Sloane, N. J. A. Sequence A002905/M2486 in "The On-Line Encyclopedia of Integer Sequences."

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Cite this as:

Weisstein, Eric W. "Polynema." From MathWorld--A Wolfram Web Resource.

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