Planar Graph (Self Doubt)

Question

This is a graph ? Is it planar or not ?

As per definition of planar graph it can be drawn in such a way that no edges cross each other.

other theorems are 

if a connected simple graph is planar→ e<=3n-6  

if a connected simple graph is planar → 2e>=3r

(e is edges , n is vertices and r is region)

here edges is 10 n is 4

e<=3n-6 (10<=6) which is wrong 

and 2e>=3r (20>=27) r is 9 .here also condition for planar graph not meet if the graph is planar but 

 

Now if i draw i dont intersect any edges .,which show it is planar 

Answer 1

we derive e<=3n-6 from statement

“In a simple undirected connected planar graph if atleast 2 edges are there then degree of each region is atleast 3.”

Simple graph means between any two vertices no parallel edges or no self loop possible. but in given graph parallel edges are possible so it is a multi-graph.

and because of which for given graph above statement is not applicable.

i hope you got it. 

Thank you.

Comments

Thank you .the theorems are all for simple graph . What i drew is a multigraph .

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yes in our GATE syllabus mostly we have Simple graphs only.