Chapter 10: Q36E (page 726)
Draw \({K_5}\) on the surface of torus (a doughnut shaped solid) so that no edges cross.
The surface of torus
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How many edges does a \({\rm{50}}\)-regular graph with \({\rm{100}}\)vertices have?
Find the chromatic number of the given graph.
Construct the dual graph for the map shown. Then find the number of colors needed to color the map so that no two adjacent regions have the same color.
Find these values a)\({x_2}\left( {{k_3}} \right)\) b) \({x_2}\left( {{k_4}} \right)\) c)\({x_2}\left( {{w_4}} \right)\) d)\({x_2}\left( {{c_5}} \right)\) e)\({x_2}\left( {{k_{3,4}}} \right)\) f)\({x_3}\left( {{k_5}} \right)\) g),\({x_3}\left( {{c_5}} \right)\) h)\({x_3}\left( {{k_{4.5}}} \right)\)
Find the chromatic number of the given graph.
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