3.(a) Draw C6, C7, We and W7. 3.(b) Are C, and W, regular graphs? Justify your answer. 3.(c) How many edges and vertices do Ce, C7, We and w, have? 3.(d) Let a, be the number of edges of W, and b, be the number of edges of Cn, Find a recurrence relation for a1, a2, az, .. and b, b2, bs, ... . Guess the explicit formula for a, and b. Justify your answer. 3.(e) For which values of n do W, and C, have Euler circuit? Justify your answer. 3.(f) For which values of n does W, have Hamiltonian circuit? If so, label the vertices and find the Hamiltonian circuit. 3.(g) For which values of n do W, and C, are bipartite? Justify your answer.

3.(a) Draw C6, C7, We and W7. 3.(b) Are C, and W, regular graphs? Justify your answer. 3.(c) How many edges and vertices do Ce, C7, We and w, have? 3.(d) Let a, be the number of edges of W, and b, be the number of edges of Cn, Find a recurrence relation for a1, a2, az, .. and b, b2, bs, ... . Guess the explicit formula for a, and b. Justify your answer. 3.(e) For which values of n do W, and C, have Euler circuit? Justify your answer. 3.(f) For which values of n does W, have Hamiltonian circuit? If so, label the vertices and find the Hamiltonian circuit. 3.(g) For which values of n do W, and C, are bipartite? Justify your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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