in Graph Theory
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Is the topic "Planarity" there in GATE 2017 syllabus?
in Graph Theory
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Yes they may ask since they ask generally combining the connectivity and planarity property.They often refer in a question frequently , "consider a simple connected planar".In such cases , u should know about planarity and its properties.
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Only knowing the properties will do?
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planarity is a fundamental topic ,you need to know to answer other related question from Graph..so you need to know it

and ya knowing basic fundamentals wil do it for you

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