Question

Draw all the connected diagrams containing four dots. There are six diagrams in total; be careful to avoid drawing two diagrams that look superficially different but are actually the same. Which of the diagrams would remain connected if any single dot were removed?

Short answer

All the connected diagrams that contain 4 dots have been drawn.

Step-by-step solution

Step 1. Given information

Configuration integral:- The configuration integral is used in probability theory, information theory and dynamical systems, it's a generalization of the definition of a partition function in statistical mechanics.

Step 2. Drawing all the diagrams in which four dots present.

(1)

(2)

(3)

(4)

(5)

(6)

Step 3. If a single dot is removed, these 3 will still remain connected.

(1)

(2)

(3)