0 votes 0 votes why in this planar graph this theorem ,”sum of degrees of faces or regions is twice the number of edges” is not true as it should hold for all planar graphs?? Note: numbers denote region or face Graph Theory graph-theory engineering-mathematics discrete-mathematics + – BHASHKAR asked Jan 5, 2019 BHASHKAR 745 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply MiNiPanda commented Jan 5, 2019 reply Follow Share When an edge lies inside a region, it contributes "2" to the degree of the region it lies within. Degree of a region is the no.of edges on the boundary. Degree(region 2)=ab+bc+cd+ad+de+de Edge de lies in region 2 and contributes 2 to the degree. So, deg of R2=6. 0 votes 0 votes Kunal Kadian commented Jan 5, 2019 reply Follow Share Degree of region 2 is $6$ not 4. Maybe you are not counting edge $de$. Also the edge $de$ should be counted twice, bcoz its both sides are exposed to region $2$ 1 votes 1 votes Please log in or register to add a comment.