6 6 votes Q.Suppose that a connected planar simple graph has 20 vertices,each of degree 3.Into how many regions does a representation of this planar graph split the plane ? ............................................................................................................ Here I am getting number of faces =36 doesn't it represent the region.? Graph Theory graph-theory + – junaid ahmad 4.3k views answer comment Share Follow Print See all 5 Comments 5 5 Comments reply Show 2 previous comments saxena0612 commented Nov 20, 2017 reply Follow flag 20 vertices 30 edges 12 regions {faces which are bounded by edges and one that is outside} 0 0 replyShare just_bhavana commented Nov 20, 2017 reply Follow flag yes 12, number of edges is 30 using handshaking lemma and then used f = e - v + 2 0 0 replyShare junaid ahmad commented Nov 20, 2017 reply Follow flag Thanks Everyone for the help :) 1 1 replyShare Please log in or register to add a comment.