In the mathematical discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices, connected with a bridge.

[1] The special case of the (2n/3,n/3)-lollipop graphs are known as graphs which achieve the maximum possible hitting time,[2] cover time[3] and commute time.

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