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QUESTION 11 Determine the adjacency matrix that represents this graph. o1 H o oo o N — — O O Y — O —~ O o —~— O O n H (B) N — — O RIOI oo —~ — O w (A) H o oo o N oo o AN O Ao <o oo O wn = (D) o o — o N — — O — Y — O —~ O o —~ — O Ox n H= ©)
QUESTION 8 A basketball competition has six teams that have completed three rounds of competition as shown. - - - [ | Bls | — | - | v | v | = Mo | v | v | = v = s — | v = v e | - - | v | = S| v = | = | v The graph to represent this information has (A) 6 edges. (B) 9 edges. (C) 15 edges. (D) 18 edges.
QUESTION 2 The total number of vertices in this graph is (A) (B) ©) (D) ~N O WD W
QUESTION 21 (5 marks) The paths connecting various landmarks in a park are shown. D P Key B Bus stop C Coffee shop D Duck pond P Playground ¢ R Rose garden R W Water feature B a) Identify one cycle that passes through the rose garden and the playground. [1 mark] b) Identify whether the graph is Eulerian or semi-Eulerian. Justify your response. [2 marks] c) Construct an adjacency matrix from the graph using the vertex order listed in the key. [2 marks]
QUESTION 4 (5 marks) The table shows the current road length (in kilometres) between six towns. v [ vern [ o | e [ R | A T [ 6 s | [ % e | e | s e | e e | s w Cwew | T s e The government plans to build a direct road between Manon and Farra. Use a network diagram to determine the length of the direct road if it is to be 4 km shorter than the length of the current shortest road route between Manon and Farra.
QUESTION 13 Four athletes Eoin (E) Fedir (F) Gede (G) and Hana (H) compete in three events: javelin (J) long jump (L) and sprints (S). Which bipartite graph represents this information? “ok J ok J F L F L G S G S H H (C) (D) oo o- - mraoantt n ron n
QUESTION 23 (5 marks) A network graph is shown. ec a) State the degree of vertex E. [1 mark] b) State the number of edges joining D and E. [1 mark] c) Construct an adjacency matrix from the graph with the vertices in alphabetical order. [3 marks]
QUESTION 3 The graph below has six vertices. The vertex with the smallest degree is A) 1 (B) 2 ©C) 3 (D) 4
QUESTION 18 Which adjacency matrix below represents the same information that is given in the network diagram? T & To (B) To (A) oo o = UOllO _ o —~ © @ — N — o o o n = =2 woI > © © — © Do -~ o o _ o © © - N — o o o n = =2 woI To (D) To ©) b o = = O UOlOl - © — @ — N — o o o N == woxL J S e —~ 8 o Do o © = _ o © —~ O N — ©o o o n == WOL]
QUESTION 2 (4 marks) A cable company is calculating the cost of laying cable between five houses (A B C D and E). The unit cost of laying the cable is $2.50 per metre. The shortest distances (in metres) between the houses are shown below. a) Construct a network diagram to represent the distances between the houses in the space provided below. [1 mark] b) Determine the minimum cost to connect all of the houses. [3 marks]
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