In the mathematical discipline of
graph theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
, the (''m'',''n'')-lollipop graph is a special type of
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
consisting of a
complete graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices ...
(clique) on ''m'' vertices and a
path graph
In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order such that the edges are where . Equivalently, a path with at least two vertices is connected and has two terminal ...
on ''n'' vertices, connected with a
bridge
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somethi ...
.
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.
See also
*
Barbell graph
*
Tadpole graph
In the mathematical discipline of graph theory, the (''m'',''n'')-tadpole graph is a special type of graph consisting of a cycle graph on ''m'' (at least 3) vertices and a path graph on ''n'' vertices, connected with a bridge
A bridge ...
References
Parametric families of graphs
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