Is a line considered a face in graph theory?

Question

For example just a straight line point to point.

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Zach Langley · Accepted Answer · 2012-04-25 21:39:55Z

up vote 3 down vote accepted

No, that is an edge. There is one face in your graph though: the unbounded or infinite face, sometimes denoted $f_\infty$.

edited Apr 25 '12 at 21:39

answered Feb 20 '12 at 2:06

Zach Langley
605514

	With a single line as your graph, is the degree of the infinite face 1 (definining the degree of a face as the number of edges encountered during a walk around the face)? – soniccool Feb 20 '12 at 2:15
	The degree of $f_\infty$ in this case is 2, since your walk uses the edge twice to return to the starting vertex. Note that the sum of all the degrees of the faces in a planar graph is always twice the number of edges. – Zach Langley Feb 20 '12 at 2:39

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