A 1-factor of a graph 
with 
graph vertices is a set of
separate graph
edges which collectively contain all 
of the graph vertices of 
among their endpoints. Harary and Palmer
(1973, p. 270) list the enumeration of 1-factors and factorizations as graphical
enumeration problems.
Graph Factor
See also
GraphExplore with Wolfram|Alpha
References
Harary, F. and Palmer, E. M. "A Survey of Graphical Enumeration Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava). Amsterdam, Netherlands: North-Holland, pp. 259-275, 1973.Referenced on Wolfram|Alpha
Graph FactorCite this as:
Weisstein, Eric W. "Graph Factor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphFactor.html