0 votes 0 votes Let G be a simple connected planar graph with 14 vertices and 20 edges. Number of closed regions in planar embedding of the graph is ? Graph Theory graph-theory graph-planarity + – Na462 asked Dec 2, 2018 recategorized Dec 2, 2018 by Mk Utkarsh Na462 3.5k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 1 votes 1 votes By Euler formula for connected planar graph, $\color{red}{n - e + f = 2}$ $n = 14$ $e = 20$ $14-20 + f = 2$ $f = 8$ In any planer graph there will be only 1 open region and rest all are closed by edges. So total closed regions = $8-1 = 7$ Mk Utkarsh answered Dec 2, 2018 selected Dec 2, 2018 by Na462 Mk Utkarsh comment Share Follow See all 3 Comments See all 3 3 Comments reply Na462 commented Dec 2, 2018 reply Follow Share Bounded region and closed region are the same thing ? 0 votes 0 votes Mk Utkarsh commented Dec 2, 2018 reply Follow Share Na462 i think so, what's the answer given? 1 votes 1 votes Na462 commented Dec 2, 2018 reply Follow Share Its correct :) 0 votes 0 votes Please log in or register to add a comment.