Finally applying the same argument one more time we conclude thatthe Euler characteristic ofGis one less than the sum of the Eulercharacteristics ofG123andG4. ThusGhas Euler characteristic 4+2-1 = 5.(3)isTrue.Suppose that a connected planar graph with 6 edgessplits the plane into 7 regions. The Euler characteristic of this graphisV-6 + 7 =V+ 1 by definition. BUt by the Euler characteristictheorem the euler characteristic of the graph must be equal to 2. SoV= 1.The correct answer is(c).square16
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