soluq2 - NAME: _____— Student ID: a MA238 Winter 2009 -...

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Unformatted text preview: NAME: _____— Student ID: a MA238 Winter 2009 - Quiz 2—a Total marks is . Answer all questions in the spaces provided. Calculators are not permitted. 3 wmarks] 1. Given the following adjacency matrix, draw the corresponding graph. A b c OHOO§ OOv—IOU— OOo—ar—xn (Dr—two} A L Wmarks] 2. Are the following graphs isomorphic? If so, give an isomorphism. If not, provide a rigorous argument that none exists. Q h gnu, {v Q C i: A Z x 3 ahA g CJW [y/marks] 3. Draw a graph with 4 verticesvthat is weakly connected but not strongly connected and has exactly 2 2626 strongly connected components. W A L~DI~0~€¢4’E J ‘/ : : 1A0? Sher-5 iv I/ Mack‘s/J '2— Vivawsib 0R C‘WM is”; “,1? W OHW WWI“? “"8 raw/LR V See Reverse 2,. 1 SimPkl. [Vmarks] 4. (a) What it mean for avgraph to be self—complementary? A SrlmVGz G {5 _$¢.{'(” Uwaeleweflfl’arj (If G and G We {’SDMor'Plu'é (b) How many edges does a selfucomplementary graph have if it has 1) vertices? v (v4) L} l [F’marks] 5. How many paths of length two are there from vertex b to vertex d for the graph with the given adjacency matrix (ordering the vertices a, b, C, d). «had “0302 “22011 A’c0130 #2402 pair 9! [Watt 2 4:,» L 4.. a r (a?) {Nib} Mr A; \h 6- :E’): 4.. C A C/ A. 1;. C V a. 7x N V’ NAME: __,___—____ Student ID: MA238 Winter 2009 — Quiz 2—b w 3 Total marks is . Answer all questions in the spaces provided. Calculators are not permitted. [flmarks] 1. Given the following adjacency matrix, draw the correSponding graph. 0.. c d a 0 1 O 0 b 1 1 1 0 C 0 0 0 1 : d 0 2 0 0 A C L Wmarks] 2. Are the following graphs isomorphic? If so, give an isomorphism. If not, provide a rigorous argument that none exists. V is owl—OFFLZL. 42(4):; 3 ‘30MO((’L:SV‘ i7 / FLA—1 M :- \/ IPLEA : 1 Wk 9 3 and L €432: [/marks] 3. Draw a graph with 5 verticethhat is weakly connected but not strongly connected and has exactly 2 ,ty/(f strongly connected components. a L; hm. V‘ 0: Mi“ S’V'arg'iip WAN V .. c- ' Ln fikmL‘HE L c are”) H (winterng Lampomwfifi‘ V WV “pg FQK‘SI2LQ . See Reverse f are ’2— U/marks] 4. (a) What it mean for a graph to be self-complementary? A 3 (3' a L? unrelemwhyj (I a Adv—"d G are Fa‘ararrb RC (b) How many edges does a self-complementary graph have if it has 1) vertices? v01) Lf 7/ Wmarks] 5. How many paths of length two are there from vertex b to vertex d for the graph with the given adjacency matrix (ordering the vertices a, b, c, d). khcd «0302 Agb3101 40130 A1202 «palms «f lush. '2— 4:”. I94». 4 : (23+) In” ea‘ihj of A1 3‘ 3(1) 4' tfil>+ 0(6)+ £61) ‘7 0| ...
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soluq2 - NAME: _____— Student ID: a MA238 Winter 2009 -...

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