Discrete Mathematics

# 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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