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Activities 14.5 Activities
Activity 14.1 .
Draw all possible simple graphs with \(4\) vertices.
Activity 14.2 .
Suppose \(G = (V,E)\) is a graph. Decide the truth of the following statement.
Every pair of a subset \(V' \subseteq V\) and a subcollection \(E' \subseteq E\) defines a subgraph \(G' = (V',E')\) of \(G\text{.}\)
Activity 14.3 .
Draw a graph where the nodes are students present in today’s class. Draw edges between pairs of students that are in the same group today. Additionally, draw an edge between a member of your group and another student if that pair was in a group together last class.
Activity 14.4 .
(a) (b) (c)
Activity 14.5 .
Consider the website Facebook as a graph where vertices are profiles and edges represent “friendship”.
(a) Should this graph be a directed graph? Why or why not?
(b) Is this graph simple? complete? Justify your answers.
(c) What does the degree of a vertex represent?
(d) Could this graph have isolated vertices?
(e)
Suppose the following graph is a subgraph of the Facebook graph.
(i) What is the largest party one of these people could throw where each party-goer is Facebook friends with every other party-goer? Justify your answer.
(ii) Assume all of the people in this graph live in the same geographic area. Which pair of non-friends are most likely to become friends in the future? Which pair of non-friends are least likely to become friends in the future? Justify your answers.
