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In the given following planar graph, what is the degree of the region R1:

nitish, what difference does it make if i keep this pendant vertex outside?

then degree of inner region will be 4 and that of outer region will be 6

As $\sum degree\ of \ region =2*edges$, means each edge will be counted twice in a region.

If edge 'ce' is inside then deg(r1)=6, if it is outside then deg(r1)=4