13 votes 13 votes In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________. Graph Theory gatecse-2021-set1 graph-theory graph-planarity numerical-answers easy 1-mark + – Arjun asked Feb 18, 2021 • retagged Nov 30, 2022 by Lakshman Bhaiya Arjun 8.1k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Here, |V| = 8 and |R| = 5 From Euler equation, for any connected planar graph (Need not to be simple) |V| + |R| = |E| + 2 always hold true. where, |V| = Number of vertices |R| = Number of faces or Regions |E| = Number of Edges hence, 8 + 5 = |E| + 2 |E| = 11 kalam_11 answered Oct 6, 2021 kalam_11 comment Share Follow See all 0 reply Please log in or register to add a comment.