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Graph Theory

Any connected group of things can be represented as a graph: cities and roads, people and friendships, and more. Learn why an even number of people have an odd number of friends.

Complete Graphs

How many distinct complete graphs are there with at least 5 and less than 10 nodes?

Note: a graph is considered complete if for any two nodes on the graph, there is an edge between them.

Let \(K_4\) be the complete graph with 4 nodes. What is the biggest degree of any node on this graph?

Note: the degree of a node is the number of edges that connect to it.

Let \(K_5\) be the complete graph with 5 nodes, how many edges does it have?

How many complete graphs with at least 1 edge and at most 50 edges are there?

Define the distance between two distinct nodes to be the fewest number of edges in a path between the two nodes. What is the largest possible distance between two distinct nodes on the complete graph with 7 nodes?

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