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Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?(a) 4(b) 0(c) 2(d) 5I have been asked this question in my homework.The above asked question is from Graphs Properties in section Graphs of Discrete Mathematics

Answer»

Right answer is (C) 2

The best explanation: We know that sum of DEGREES of all vertices = 2X no of edges. Say number of edges is E. Degree of LAST vertex is x, 1+2+3+4+5+6+7++8+9+x = 2XE

=>45+x = 2XE

Now putting options we get answer 0 or 5

But one vertex of degree 9 means it connected to all other VERTEXES. So, the degree must be 5.


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