A group of 8 friends played one-on-one ping pong last night. Tom, one of the fri

Question

A group of 8 friends played one-on-one ping pong last night. Tom, one of the friends, kept track of which friends played each game during the evening, and the next day drew a graph where each vertex represented one of the 8 friends and where each edge represented that the friends played a game against each other last night. (Note: The following situations may not be possible, but can still reasonable be interpreted.) a. Interpret what it would represent for the graph to have multiple edge in this context b. Interpret what it would represent for the graph to have a loop would in this context. C. Suppose that the vertex corresponding to Rose, one of the friends, has an eccentricity of 1 in the graph, interpret what this represents in this context. d. Suppose that the vertex corresponding to Tom has a degree of 5 in the graph, interpret what this represents in this context. e. Suppose that the graph is disconnected, interpret what this represents in this context.

Explanation / Answer

a. Each of the friends may have played one or multiple games with other friends.

b. One of the friends may have played with himself (quite not possible).

c. This mean Rose have played with each of the other 7 friends.

d. Tom must have played with 5 other friendss OR (Tom have played once with himself , and 3 games with three other friends).

e. One or maybe more than one of friends have not played a single game.

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