Determine the density of a planar graph with 34 edges and 13 nodes.(a) 22/21(b) 12/23(c) 328(d) 576I have been asked this question in a national level competition.This question is from Planarity, Degree and Coloring of Graph in portion Graphs of Discrete Mathematics

Determine the density of a planar graph with 34 edges and 13 nodes.(a)

1.	Determine the density of a planar graph with 34 edges and 13 nodes.(a) 22/21(b) 12/23(c) 328(d) 576I have been asked this question in a national level competition.This question is from Planarity, Degree and Coloring of Graph in portion Graphs of Discrete Mathematics
Answer» The correct answer is (a) 22/21 The explanation: The density of a planar graph or network is described as the ratio of the number of EDGES(E) to the number of POSSIBLE edges in a network with(N) nodes. So,D = E − N + 1/ 2 N − 5. Hence, the required answer is: D=(34-13+1)/(2*13-5) = 22/21. A completely sparse planar graph has density 0 and a completely DENSE planar graph has degree 1.

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