Suppose that an airline offers daily non-stop flights as follows: there are thre

Question

Suppose that an airline offers daily non-stop flights as follows: there are three flights from New York to Miami, two flights from Miami to New York, One flight from Miami to Chicago, two flights from Chicago to Miami, 3 flights from Chicago to New York, one flight from New York to Houston and one flight from Houston to New York, two flights from Houston to Miami, and one flight from Miami to Houston.

(a). Is this a complete graph ? Why or why not ? If not explain how you could " complete the graph" by adding an edge or edges. Is this a bipartite graph? Why or why not? If not, explain how you could "maKe the graph bipartite" by removing an edge or edges ( find a bipartite subgraph).

So far i have 7 edges for Mia, 6 for NY, 4 for Chi and 2 for Hou. Please help

Explanation / Answer

Suppose that an airline offers daily non-stop flights as follows: there are three flights from New York to Miami, two flights from Miami to New York, One flight from Miami to Chicago, two flights from Chicago to Miami, 3 flights from Chicago to New York, one flight from New York to Houston and one flight from Houston to New York, two flights from Houston to Miami, and one flight from Miami to Houston. we need the same in and out. Outs = -1, In = +1 NY=-3, Miami = +3 NY=-1, Miami=+1 NY=-1, Miami=0, Chicago=+1 NY=-1, Miami=+2, Chicago=-1 NY=+2, Miami=+2, Chicago=-4 The next two cancel out. NY=+2, Miami=+4, Chicago=-4, Houston: -2 NY=+2, Miami=+3, Chicago=-4, Houston: -1 So we can add two more flights from New York to Chicago to get: NY=0, Miami=+3, Chicago=-2, Houston: -1 add two more flights from Miami to Chicago to get: NY=0, Miami=+1, Chicago=0, Houston: -1 And one final flight from Miami to Houston.

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