19 votes 19 votes Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is: $6$ $8$ $9$ $13$ Graph Theory gatecse-2005 graph-theory graph-planarity + – gatecse asked Sep 21, 2014 • edited May 30, 2018 by kenzou gatecse 9.3k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply rahul sharma 5 commented Jun 17, 2017 reply Follow Share Why is it marked out of syllabus?Is graph theory is not in syllabus? 1 votes 1 votes Rohit kathuria commented Nov 30, 2017 reply Follow Share its in 0 votes 0 votes Please log in or register to add a comment.
Best answer 25 votes 25 votes $f=e-n+2$ where $f$ denotes number of faces E the number of edges $n$ the number of vertices So $f=19-13+2 = 8$ faces Correct Answer: $B$ Bhagirathi answered Sep 21, 2014 • edited Apr 23, 2019 by Naveen Kumar 3 Bhagirathi comment Share Follow See all 2 Comments See all 2 2 Comments reply sripo commented Sep 27, 2018 reply Follow Share Being simple graph cant we use the formula 3*R<=2*E if we use this then answer turns out to be 13.Please tell me what is wrong in my logic. 0 votes 0 votes Arpit Patel commented Jan 10, 2022 reply Follow Share For k components, e – n + (k+1) = f For connected, k=1 e-n+2=f 1 votes 1 votes Please log in or register to add a comment.
4 votes 4 votes f=e-n+(k+1) f=number of faces, e=number of edges, n=number of vertices, k=number of connected components, for connected graph k=1,so f=e-n+(1+1) f=e-n+2 f=19-13+2 f=8 talha hashim answered Dec 10, 2018 talha hashim comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Answer will be (b) 8 because f+v-e = 2 for connected graph f = 2+6 = 8 f is the no. of regions or faces e is the number of edges v is the number of vertices Pratyush Priyam Kuan answered Feb 20, 2020 Pratyush Priyam Kuan comment Share Follow See all 0 reply Please log in or register to add a comment.