2 2 votes If G is a 3-regular, connected, simple, planar graph with 18 vertices, then, the number of regions in G are -- ?10382011 Graph Theory discrete-mathematics goclasses goclasses-cs-dpp goclasses-cs-dpp-day-278 goclasses-dm-practice-questions graph-theory + – GO Classes 269 views answer comment Share Follow Print 0 reply Please log in or register to add a comment.
2 2 votes By using the formula 1. 2*e = summation of degrre of all vertices (handshaking lemma) 2. n - e + R = 2 (Euler formula) This line is really matter 3 regular connected means every vertices has degree 3 which forms an equaltion 3*v = 2*e e = 27 subtituting it in euler formula we get n - e + R = 2 . 18 - 27 + R = 2 . R = 9 + 2 = 11. so option D is correct. akash_kumar 9 answered May 23 akash_kumar 9 comment Share Follow See 1 comment 1 1 comment reply arindam_roy 1 commented Jul 15 reply Follow flag From the question 3- regular we can find the number of edges d(vi)=2e; 3*18=2e; ..e=27 ; after finding the number of eges we can simply use the eulers fromula (v+f=e+c) and get the number of faces .. so , the answer is option D 0 0 replyShare Please log in or register to add a comment.
0 0 votes If G is a 3-regular, connected, simple, planar graph degree of every vertex= 3summation of degree of all vertices= 2 $\times$ E3$\times$18 =2EE=27by euler formula for connected planar graph V+F=E+2F=11 Parineta answered Sep 19 Parineta comment Share Follow 0 reply Please log in or register to add a comment.
