0 votes 0 votes Consider the graph G given below. The graph G is (a) planar (b) non- planar Others discrete + – mathematics asked Oct 19, 2017 mathematics 513 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Prashant. commented Oct 19, 2017 reply Follow Share it is non-plannar. Assume graph is plannar since it contain triangle . so e<=2n-4 i.e. e<=12 but here e is not less than equal to 12 . so it is non plannar. 1 votes 1 votes Shubhanshu commented Oct 19, 2017 reply Follow Share @Prashant. I am agree that this is not a plannar graph. But, this graph satisfing all three conditions:- v-e+r = 2 // r = no of regions kr<= 2e $e<= \frac{k(v-2)}{k-2}$ // k = min degree of the region. 0 votes 0 votes srestha commented Oct 19, 2017 reply Follow Share @Prasant It will be planar chk again 0 votes 0 votes Prashant. commented Oct 19, 2017 reply Follow Share it is not plannar. draw without cross edge. 0 votes 0 votes Shubhanshu commented Oct 19, 2017 reply Follow Share If it is planar then why we use those three conditions. This is contradicting those 3 conditions. 0 votes 0 votes srestha commented Oct 19, 2017 i edited by srestha Oct 19, 2017 reply Follow Share have a look 0 votes 0 votes Shubhanshu commented Oct 19, 2017 reply Follow Share I got it, It is a planar graph. Check this:- Let me know what is wrong in this. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes (a) It's a planar graph Image credit: @Shubhanshu amaity answered Oct 19, 2017 • edited Oct 19, 2017 by amaity amaity comment Share Follow See all 2 Comments See all 2 2 Comments reply Shubhanshu commented Oct 19, 2017 reply Follow Share @amaity check the above comments. 0 votes 0 votes amaity commented Oct 19, 2017 reply Follow Share Thanks @Shubanshu for pointing out the mistake. I have corrected it. 0 votes 0 votes Please log in or register to add a comment.