Homework Answers
a) We know that a path between two vertices is a sequence of edges such that both the vertices and the edges in the sequence are distinct. Therefore, the number of paths from a to c in this graph is 4.
b) We know that a trail between two vertices is a sequence of
edges such that only the edges are distinct. Therefore, the number
of paths from a to c in this graph is 
.
c) We know that a walk between two vertices is a sequence of edges. Therefore, since we can make infinite sequences of edges from a to c, the number of walks from a to c is infinite.
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Consider the following graph. ei e2 es a e3 b e4 i (a) How many paths...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4,...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]), (e4, (v4,v1)), (e5,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. How many edges are in a spanning tree for graph G? What is the weight of a minimum-weight spanning tree for the graph G if the weight of an edge is defined to be W (ei) L]?
Suppose a sample space consists of five elementary outcomes e1, e2, e3, e4, e5with the characteristics...
Suppose a sample space consists of five elementary outcomes e1, e2, e3, e4, e5with the characteristics that e1, e4, and e5are equally likely, e2is twice as likely ase1and e3is four times as likely as e1. a. DetermineP(ei) for i = 1, 2, ... 5 b. IfA = {e3, e4}, find P( A ).
Consider the following energy levels of a hypothetical atom: E4 −2.21 × 10−19 J E3 −6.41...
Consider the following energy levels of a hypothetical atom: E4 −2.21 × 10−19 J E3 −6.41 × 10−19 J E2 −1.15 × 10−18 J E1 −1.65 × 10−18 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4? × 10 m (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? × 10 J (c) When an electron drops from the...
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points....
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points. The following probability assignments apply: p(E1 )=.05 p(E2)=.20 P(E3)=.20 p(E4)=.25 p(E5)=.15 p(E6)=.10 and p(E7)=.05 Let A={E1,E4,E6} B={E2,E4,E7} C= {E2,E3,E5,E7} 1) Find A ∩ B and P(A ∩ B) and Are events A and C mutually exclusive?
Be sure to answer all parts. Consider the following energy levels of a hypothetical atom: E4...
Be sure to answer all parts. Consider the following energy levels of a hypothetical atom: E4 −2.11 × 10−19 J E3 −5.61 × 10−19 J E2 −1.05 × 10−18 J E1 −1.85 × 10−18 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4? × 10 m (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? × 10 J (c)...
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42...
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42 UE U2 26 07 Us •14 ez, e4, es, and es e, and e ez, ez, e4, and e6 en, ez, e4, es, e6, and en
consider the beam and the loading Question #3: (8 marks/20) I/I BET el, e2 and e3)...
consider the beam and the loading
Question #3: (8 marks/20) I/I BET el, e2 and e3) Consider the beam and the loading shown in the following figure (Figure #3). Determine: 1- The reactions at the roller A and the pin B. [ABET: el- 4 Marks] 2- The shear force and bending moment at point C. [ABET: e3-2 Marks] 3- The shear force and bending moment at point D. [ABET: e3- 2 Marks] 500 lb 200 lb 300 lb
Graphs (15 points) 14. For the following graph (8 points): a. Find all the edges that...
Graphs (15 points) 14. For the following graph (8 points): a. Find all the edges that are incident of v1: b. Find all the vertices that are adjacent to v3: C. Find all the edges that are adjacent to e1: d. Find all the loops: e. Find all the parallel edges: f. Find all the isolated vertices: g. Find the degree of v3: h. Find the total degree of the graph: e3 e2 V2 VI 26 e4 e7 es 05...
Let G be the graph ei U1 e2 and consider the walk V111221 (a) Can this...
Let G be the graph ei U1 e2 and consider the walk V111221 (a) Can this walk be written unambiguously as V1 V2V1? O Yes O No If this walk cannot be written unambiguously, select the walk that V1VzVcould equally refer to, but is different than vierzez 1 OviezV21V1 OeVie2291 OeVie1422 O vze.V1212 The walk v1V 2V1 is unambiguous. (b) Can this walk be written unambiguously as e, ez? O Yes O No If this walk cannot be written unambiguously,...
Let G be the graph ei UL U2 e2 and consider the walk ve vze2V1 (a)...
Let G be the graph ei UL U2 e2 and consider the walk ve vze2V1 (a) Can this walk be written unambiguously as V1 V2V1? Yes No If this walk cannot be written unambiguously, select the walk that v1V2V1 could equally refer to, but is different than vje, vzezV1 vie221V1 O v2e11e2V2 O eV11122 evezV21 The walk v1V 2V1 is unambiguous. (b) Can this walk be written unambiguously as e ez? Yes O No If this walk cannot be written...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]), (e4, (v4,v1)), (e5,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. How many edges are in a spanning tree for graph G? What is the weight of a minimum-weight spanning tree for the graph G if the weight of an edge is defined to be W (ei) L]?
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42 UE U2 26 07 Us •14 ez, e4, es, and es e, and e ez, ez, e4, and e6 en, ez, e4, es, e6, and en
consider the beam and the loading
Question #3: (8 marks/20) I/I BET el, e2 and e3) Consider the beam and the loading shown in the following figure (Figure #3). Determine: 1- The reactions at the roller A and the pin B. [ABET: el- 4 Marks] 2- The shear force and bending moment at point C. [ABET: e3-2 Marks] 3- The shear force and bending moment at point D. [ABET: e3- 2 Marks] 500 lb 200 lb 300 lb
Graphs (15 points) 14. For the following graph (8 points): a. Find all the edges that are incident of v1: b. Find all the vertices that are adjacent to v3: C. Find all the edges that are adjacent to e1: d. Find all the loops: e. Find all the parallel edges: f. Find all the isolated vertices: g. Find the degree of v3: h. Find the total degree of the graph: e3 e2 V2 VI 26 e4 e7 es 05...
Let G be the graph ei U1 e2 and consider the walk V111221 (a) Can this walk be written unambiguously as V1 V2V1? O Yes O No If this walk cannot be written unambiguously, select the walk that V1VzVcould equally refer to, but is different than vierzez 1 OviezV21V1 OeVie2291 OeVie1422 O vze.V1212 The walk v1V 2V1 is unambiguous. (b) Can this walk be written unambiguously as e, ez? O Yes O No If this walk cannot be written unambiguously,...
Let G be the graph ei UL U2 e2 and consider the walk ve vze2V1 (a) Can this walk be written unambiguously as V1 V2V1? Yes No If this walk cannot be written unambiguously, select the walk that v1V2V1 could equally refer to, but is different than vje, vzezV1 vie221V1 O v2e11e2V2 O eV11122 evezV21 The walk v1V 2V1 is unambiguous. (b) Can this walk be written unambiguously as e ez? Yes O No If this walk cannot be written...
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