1 votes 1 votes Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to: $3$ $4$ $5$ $6$ Graph Theory nielit2016dec-scientistb-cs discrete-mathematics graph-theory graph-planarity + – admin asked Mar 31, 2020 • retagged Oct 23, 2020 by Krithiga2101 admin 1.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes "G is a connected graph", "on the plane" => so the graph is planar and connected Theorem 1 (Euler's Formula) Let G be a connected planar graph, and let n, m and f denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then n - m + f = 2. 10 - 15 + f =2 => f =7 One of the face is non bounded so, answer is 6. Ref: http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/planarity.htm smsubham answered Apr 1, 2020 smsubham comment Share Follow See 1 comment See all 1 1 comment reply manisha11 commented Sep 16, 2020 reply Follow Share Thanks for sharing this, out of all faces 1 face is unbounded 0 votes 0 votes Please log in or register to add a comment.
