# Doc9 - 8 a If a tree has four vertices of degree 2 one...

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Unformatted text preview: 8. a] If a tree has four vertices of degree 2. one vertex of de- gree 3, two of degree 4. and one of degree 5. how men},r pendant 1rertiees does it have? b] If a tree T = (V, E} has 1:; 1Iret'tieee. of degree 2, 113, ver- tices of degree 3. . . . , and um vertiees of degree m. what are |V| and |E|‘? 12. Let G = (V. E} be a loop-free connected undirected graph where V = {U[. U2.1U_1.. .._, v..}.n :_=- 2.deg{v1}=l,and degtv.) a 2 for 2 5 t‘ :i n. Prove that G must have a cycle. 16. For each graph in Fig. 12.1 determine how men}.r noniden— tiea] {though some Ina},-r be isomorphic) spanning trees exist. 20. Complete the proof of Theorem 12.5. T. a} Find the depth-ﬁrst spanning tree for the graph shown in Fig. 11.72I[a} if the order of the vertices is given as (i) a, b, c. d, e, f, g. It; (ii) is, g, f, e, ti. c, E}, :1; (iii) a, b, c, d. h. g, f, e. b] Repeat part {a} far the graph shown in Fig. 11.35[i). 8. Find the breadth—ﬁrst spanning ﬂees for the graphs and pre— scribed crders given in Exercise T". 14. The complete binary tree T = (V, E} has V = {a, b. c, . . . _ i. j. it}. The pesterder listing of V yields 11‘, e. b, h. 1'. f? j. k, g? L‘._. a. From this infcnnaticn draw T if {a} the height of T is 3; (b) the height of the left subtree of T is 3. 21}. Let T = (ifT E } be a balanced cemplete m—ary tree cf height h 3 2. If T has t’ leaves and big. internal rertices at level}: — I. explain whyr E = ml" + [m — llbh_l. ...
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## This note was uploaded on 10/01/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

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Doc9 - 8 a If a tree has four vertices of degree 2 one...

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