Simple & Connected Graph Definitions for Exam Tomorrow

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A simple graph is defined as an undirected graph that contains no loops or multiple edges between the same two vertices. A connected graph is characterized by the presence of a path that links all vertex points within the graph. These definitions are essential for understanding basic graph theory concepts. The user requested these definitions for an upcoming exam without the need for proofs. Clear and concise definitions are crucial for effective study and recall.
terryfields
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just need 2 definitions without proof for an exam tomorrow, don't need to use them for anything just need to be able to quote them but can't find them anyway so if someone could helpfully write them down that would be great
1)simple graph
2)connected graph

cheers
 
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terryfields said:
just need 2 definitions without proof for an exam tomorrow, don't need to use them for anything just need to be able to quote them but can't find them anyway so if someone could helpfully write them down that would be great
1)simple graph
2)connected graph

cheers

Simple Graph - an undirected graph with no loops or multiple edges between the same two vertices.

Connected Graph - a graph in which all vertex points are joined by a path
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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