Imagine a simple undirected graph with the maximum number of…

Imagine a simple undirected graph with the maximum number of edges. Which representation would be the better option for this graph: an adjacency matrix or an adjacency list? Justify your answer, including the time complexity for edge lookup AND the space complexity (in Big O) of the data structures. Use n for the cardinality of the set of vertices, and m for the cardinality of the set of edges.

Let G be an undirected graph whose vertices are the integers…

Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: Vertex Adjacent Vertices 1 (2, 3, 8) 2 (1, 3, 4)  3 (1, 2, 4) 4 (2, 3, 6) 5 (6, 7, 8) 6 (4, 5, 7) 7 (5, 6, 8) 8 (1, 5, 7) Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. Give the sequence of vertices of G visited using a BFS traversal starting at vertex 1.

Your distance from lightning varies directly with the time i…

Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 16 seconds after you see the lightning, you are about 4 miles from the lightning.   a. Write a direct variation equation for the relationship between time and distance.     b. Estimate how many seconds it would take for the thunder to travel a distance of 4 miles.  

Heart rates and life spans of most mammals are inversely rel…

Heart rates and life spans of most mammals are inversely related. A cat lives for about 30.4 years on average and has a heart rate of 252 beats per minute. a. What is the constant of variation?     b. A hamster has a heart rate of about 317 beats per minute. About how long will ahamster live?     c. An elephant lives for about 70 years. About how many times per minute does anelephant’s heart beat?