planar graph

Question

Is this a planar graph ?

Comments

yes, given graph is planar, it is isomorphic to below planar graph

sorry, for the rough diagram.

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another way will be to solve by Euler's theorem

e<=3v-6;

v=8;e=12; now 12<18; so it is planer

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acually this way you can prove gragh is non planner if condition is not satisfied.

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@anu u mean if it is not satisfied it is non planar

but if its satisfied doesnt necesarily neeed to be a planar graph ?

Answer 1

The given graph is planar as it can be redrawn such that not a single edge intersects any other edge

            3 --------------------------------------- 2

            l.    \.                            /.        l

            l.          0 ---------------1             l

            l.          |                    |              l

            l           7 ---------------6             l

            |.    /.                           \.        l

            4 -------------------------------------- 5