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Unformatted text preview: 5. Fer rt 3 2, let G = (V. E ) he the leepfree undirected
graph, where V is the set ef binary ntuples [ef 0’s and 1’s}
and E = {{u, w}v. tn E V and 1:, ts differ in [exactly] twe
pesitiens}. Find MG). '1". SEVEN tewns rt, h, c, d, c, If, and g are connected by a sys
tem ef highways as fellews: (1) 122 gees frent a te c, passing
threugh b; (2}133 gees frern c re d and then passes threttgh b
as itcentinues te f ; [3} [44 gees fretn d threugh s te n; [4] I55
gees item f In is, passing threugh g; and [5) 1—65 gees from g
to d . ll]. Give an example ef a cennected graph G where rernevittg
an}? edge ef G results in a discnnnected graph. 12. a] If G = (V. E) is an undirected graph 1with V = v. E = e, and ne leeps, prese that 2.9 1: u1 — 1.1. h) State the eert'espettding, inequality»r fer the case when G
is directed. 3. a] Haw man}r spanning subgraphs are there fer the graph
G in Fig. ll.2?(a}? h} Haw many ednneeted spanning suhgraphs are [here it]
Part (a)? e) Haw man}r ef the spanning subgraphs in part (a) have
vertex {4 as an isolated vertex?I 15. Find all [leapfree} nenisemerphie undireeted graphs with
fear vertiees. Haw many of these graphs are connected“? 12. a} Let G be an undirected graph with n vertiees. If G is isn—
marphie ta its awn complement 6+ haw manyr edges must
G hawe‘.l (Sueh a graph is ealled seiﬁeempfemeatary.) h} Find an example of a selfeemplementaiy graph an four
1l'ertiees and one em ﬁve vertiees. e} If G is a self—eemplementary graph en a vertiees, where
a e: Lpreve thatn = 4!: are = M: + 1, far semefr E T“. ...
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 Spring '08
 PEARCE

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