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Discrete MathematicsAn undirected graph has 8 vertices labelled 1, 2, \dots, 8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8? (i) 15 (ii) 8 (iii) 5 (iv) 2320222mDesign & Analysis of AlgorithmsThe minimum number of colors needed to color a graph having n > 3 vertices and 2 edges is: - (i) 2 - (ii) 3 - (iii) 4 - (iv) 120232mDesign and Analysis of Algorithms The minimum number of colors needed to color a graph having n > 3 vertices and 2 edges is (i) 2 (ii) 3 (iii) 4 (iv) 120222mDesign & Analysis of AlgorithmsConsider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three? - (i) 1/8 - (ii) 1 - (iii) 8 - (iv) 820192m
PreviousIf C_n is the nth cyclic graph, where n>3 and n is odd, determine the value of \chi(C_n). (i) 32572 (ii) 16631 (iii) 3 (iv) 310Next(a) Let D = \{-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36\} Determine which of the following statements are true and which are false. Provide counterexamples for those statements that are false. (i) \forall x \in D, if x is odd, then x > 0 (ii) \forall x \in D, if x is less than 0, then x is even (iii) \forall x \in D, if x is even, then x \le 0
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