Degree of a Face in a Plane Graph | Graph Theory

What is the degree of a face in a plane graph? And how does the degree sum of the faces in a plane graph equal twice the number of edges? We'll go over definitions and reasoning in today's graph theory lesson!

The degree of a region, or face, of a plane graph is the number of edges in the boundary, sort of. We have to be very careful about our definitions. Watch the full lesson for details! We end up defining the degree of a face of a plane graph as the number of edges traversed (as in, the length) in a shortest closed walk that contains all edges of the boundary of the face. This ensures that edges that lie on cycles will be counted once in the degrees of two different faces, and edges that do not lie on cycles will be counted twice in the degree of one face. Thus, every edge will be counted twice!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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[nunu.g]

I have discrete exam tommorow and you have no idea you just saved my life God bless u sir🙏🙏

[leolyo]

Could you do a lesson on Chromatic Polynomials perhaps?

[SHASHANKRUSTAGII]

This is second handshaking lemma.
watched NPTEL IISER PURE GRAPH THEORY LECTURES on this.

[gnagyusa]

Cool explanation. Thanks! I've written a polygon mesh 3D boolean operation tool for my 3D software, and I'm always looking for new insights related to the field that might help me improve it.

[divyatailor]

I have a doubt from sets:
Given that if A is a subset of B, then C-B is a subset of C-A. Is the reverse proof true?