A connected planar graph consists of exactly 12 vertices and divides the plane into exactly 8 distinct regions (including the outer face). Calculate the exact number of edges present in this graph, and determine the theoretical maximum number of edges this graph could possess while remaining planar.

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Mathematics · Graph Theory - Planar Graphs

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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18 edges present; 30 maximum edges allowed

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Answer 1

22 edges present; 30 maximum edges allowed

Answer 2

18 edges present; 24 maximum edges allowed

Answer 3

20 edges present; 36 maximum edges allowed

Answer 4

18 edges present; 30 maximum edges allowed

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