Lollipop graph

{{infobox graph | name = Lollipop graph | image = | image_caption = A (8,4)-lollipop graph | vertices = $$m+n$$ | edges = $$\tbinom m2 + n$$ | girth = $$\left\{\begin{array}{ll}\infty & m \le 2\\ 3 & \text{otherwise}\end{array}\right.$$ | notation = $$L_{m,n}$$ | properties = connected }}

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.

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