Unformatted text preview: is ni -1. Thus, the total number of edges is (nl - 1) + (n2 - 1) + . .. + (nc -1) = n - c. 27. (a) [BB] Using Corollary 12.1.7, we have Ldeg(vi) ~ 8, so the tree has at least four edges and hence at least five vertices. If the result is not true, then there are two vertices of degree 3, at most three vertices of degree 1, and the rest have degree at least 2. Then Ldegvi ~ 2(3) + 3(1) + (n - 5)2 = 2n -1, contradicting the fact that L deg Vi = 2 (n - 1). (b) Here is a tree with two vertices of degree 3 and exactly four vertices of degree 1. Exercises 12.2 1. [BB] We show T and two other spanning trees found by adding a and then successively deleting f and 9 are shown to the right. 2. (a) [BB] Here is one possible answer. The second and third trees are isomorphic, but neither is isomorphic to the first. T a 4 5 a...
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- Summer '10
- Graph Theory, NC, Planar graph, vertices, Bipartite graph