4. In a round-robin tournament the SKT T1 beat the Invictus Gaming, the SKT T1 beat the TSM, the SKT T1 beat the Fnatic, the Invictus Gaming beat the TSM, the Invictus Gaming beat the Fnatic, and the TSM beat the Fnatic. Model this outcome with a directed graph. 5. The number of edges in a regular graph of degree 46 and 8 vertices is a) 347 b) 230 c) 184 d) 18
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- If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify1. Draw the following graph and answer the three questions below.V ={Red, Yellow, Green}, where each node represents a color state of a traffic light system.E = {(Red, Yellow), (Yellow, Green), (Green, Red), (Red, Green), (Red, Yellow)}, where the edges represent transitions from one traffic light state to another.(a) Is it a directed graph or undirected graph?(b) Which of the transitions (edges) do not make sense in practice? For example, does ayellow light follow a red light in traffic?(c) Modify the set of edges (E) and show the correct traffic light transitions in a corrected graph.Q1- What is the minimum distance between points C and F? Q2- Which of the following is a Hamiltonian Circuit for the given graph? Q3- What is the length of the Hamiltonian Circuit described in Q2? Q4- Which vertex in the given graph has the highest degree?
- how can I prove that "if G has no isolated vertices and has a walk that uses all the edges, then G is connected."1- Show an example of a subgraph, spanning subgraph, induced subgraph of the complete graph in following question Draw the following graph and answer the three questions below.V ={Red, Yellow, Green}, where each node represents a color state of a traffic light system.E = {(Red, Yellow), (Yellow, Green), (Green, Red), (Red, Green), (Red, Yellow)}, where the edges represent transitions from one traffic light state to another.(a) Is it a directed graph or an undirected graph?(b) Which of the transitions (edges) do not make sense in practice? For example, does a yellow light follow a red light in traffic?(c) Modify the set of edges (E) and show the correct traffic light transitions in a corrected graph.a) List all the odd vertices of the graph.b) According to Euler’s Theorem, does the graph have an Eulerian circuit? Howdo you know?c) According to Euler’s Theorem, does the graph have an Eulerian path? Howdo you know? What is the difference between a Hamiltonian path and an Eulerian path? A person starting in Columbus must-visit Great Falls, Odessa, andBrownsville (although not necessarily in that order), and then return home toColumbus in one car trip. The road mileage between the cities is shown Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex. Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in…
- Mo. For each of the following shaded region in Figure 1, can it be the feasible region of a linear program? The subject is discrete math Part III. Determine the number of vertices and edges and find the in-degree and out-degree of each vertex for the given directed multigraph.Hey, The condensation of a graph G with k strong coherence components G1 =.(V1 , E1 ), . . . , Gk = (Vk , Ek )is the reduction of the original graphto its strong coherence components. In this case, the coherence components are combined into one node each in the condensation. The condensation to G is thus the graph G↓=({V1,...,Vk},E),where(Vi,Vj)∈E ⇔i̸=j∧∃u∈Vi,v∈Vj:(u,v)∈E holds. what is the Kondensation G↓ of the graph in the picture? Thank you in advance!
- In Cay({(1, 0), (0, 1)}:Z4 ⊕ Z5), find a sequence of generators thatvisits exactly two vertices twice and all others exactly once and returnsto the starting vertex."If G has a walk that uses all the edges, then G is connected." I know that this statement is false but how can I prove that it is false?Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown.