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12.2 Graph Structures
Degree sums and their link to edge count, complete graphs, subgraphs, cycles, and counting the triangles and cliques hidden inside a network.
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2 exercises
12.2 Exercise 5
Use the Sum of Degrees Theorem to determine the number of introductions required in a room with
- 6 strangers.
- 10 strangers.
- strangers.
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12.2 Exercise 11
The graphs in YOUR TURN 12.6 represent social communities. The vertices are individuals and the edges are social connections. Use the graphs to answer the questions.
- Which graph has the most triads? Name the triangles.
- Which graph has the fewest triads? Name the triangles.
- How might an increase in the number of triads in a graph affect the resilience of a community? Explain your reasoning.
- Identi…
2.5
Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.