There appears to be no standard term for a simple connected graph with exactly edges , though the words "polynema"
(Kyrmse) and "polyedge " (Muñiz 2011)
have been proposed. The numbers of A002905 ).
An vertices , where 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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References Gardner, M. "The Problem of the Six Matches." In The
Unexpected Hanging and Other Mathematical Diversions. Kyrmse, R. "Polynemas."
https://www.oocities.org/kyrmse/POLIN-E.htm . Muñiz,
A. "Puzzle Zapper Blog: Pentaedges." Apr. 10, 2011. https://puzzlezapper.com/blog/2011/04/pentaedges/ . Sloane,
N. J. A. Sequence A002905 /M2486
in "The On-Line Encyclopedia of Integer Sequences." Referenced
on Wolfram|Alpha Polynema
Cite this as:
Weisstein, Eric W. "Polynema." From MathWorld https://mathworld.wolfram.com/Polynema.html
Subject classifications
edges, though the words "polynema"
(Kyrmse) and "polyedge" (Muñiz 2011)
have been proposed. The numbers of 
-polynemas for 
, 2, ... are 1, 1, 3, 5, 12, 30, 79, 227, ... (OEIS A002905).
-polynema has 
vertices, where 
is its circuit
rank.
