27 27 votes K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs? K4 is a planar while Q3 is not Both K4 and Q3 are planar Q3 is planar while K4 is not Neither K4 nor Q3 is planar Graph Theory gatecse-2011 graph-theory graph-planarity normal + – go_editor 11.6k views answer comment Share Follow Print See all 3 Comments 3 3 Comments reply Nisha Bharti commented Jan 12, 2023 reply Follow flag For planarity check we can use the property m<=2n-4 then why the result of K4 is 6<=4 means it is not planar 0 0 replyShare Thadymademe commented Sep 6, 2023 reply Follow flag @Nisha Bharti we use e <= 2v – 4 only when we have connected planar graph with v>=3 and there is no cycle in form of triangle in the graph although the graph can be cyclic . In , general , for any connected planar graph with v>=3 , we can say that :- e <= 3v-6 . where e is the number of edges and v is the number of vertices . 5 5 replyShare Raj_Dev_Verma commented Jul 6 reply Follow flag Both are planar 0 0 replyShare Please log in or register to add a comment.
Best answer 45 45 votes (B) Both are Planar graphs Both graphs can be drawn on a plane without having any crossed edges. $\text{Showing $K_{4}$ is Planar}$ $\text{Showing $Q_{3}$ is Planar}$ Manu Thakur answered Nov 19, 2014 • edited May 10, 2019 by Lakshman Bhaiya Manu Thakur comment Share Follow See all 3 Comments 3 3 Comments reply Kishan K. Verma commented Dec 28, 2017 reply Follow flag Please explain how Q3 can be drawn without crossing edges. @Manu Thakur 0 0 replyShare Manu Thakur commented Dec 28, 2017 reply Follow flag kishan, now check. 0 0 replyShare Kishan K. Verma commented Dec 29, 2017 reply Follow flag Thanks. Got it. 0 0 replyShare Please log in or register to add a comment.
3 3 votes K4 and Q3 are graphs with the following structures . akshay_123 answered Sep 3, 2023 akshay_123 comment Share Follow 0 reply Please log in or register to add a comment.
1 1 vote Drawing an alternate graph will take lots of time; a better way is to put the value in the equation e<=2n-4 and check validity. Surya013 answered Sep 25, 2025 • edited Jan 11 by Surya013 1 flag: ✌ Low quality (Rhino “wrong concept”) Surya013 comment Share Follow See 1 comment 1 1 comment reply Rhino commented Jan 10 reply Follow flag If the graph is planar then e<=3n-6 (n>=3), vice versa may not be true. Ex: Take K3,3 n=6, e=9 condition satifies, but it is not Planar. 1 1 replyShare Please log in or register to add a comment.
0 0 votes ans both are planer becoz not intersect zgod answered Dec 25, 2025 zgod comment Share Follow 0 reply Please log in or register to add a comment.
