The size of a minimum edge cover in a graph 
is known as the edge cover number of
, denoted 
.
If a graph 
has no isolated points, then
 |
where 
is the matching number and 
is the vertex count of
(Gallai 1959, West 2000).
Edge Cover Number
See also
Edge Cover, Edge Cover Polynomial, Minimum Edge CoverExplore with Wolfram|Alpha
References
Gallai, T. "Über extreme Punkt- und Kantenmengen." Ann. Univ. Sci. Budapest, Eőtvős Sect. Math. 2, 133-138, 1959.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.Cite this as:
Weisstein, Eric W. "Edge Cover Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EdgeCoverNumber.html