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Famous Graphs and Their Properties
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Petersen Graph
A specific graph with 10 vertices and 15 edges which is cubic and non-planar. Significance: Often used as a counterexample in graph theory problems.
Barbell Graph
Combined of two complete graphs (cliques) connected by a path. Significance: Used to study bottleneck problems and network connectivity.
Bipartite Graph (Km,n)
A graph whose vertices can be divided into two disjoint sets such that each edge connects a vertex in one set to one in the other set. Significance: Used to model relationships that bipartition naturally.
Complete Graph (Kn)
A graph in which every pair of distinct vertices is connected by a unique edge. Significance: Used as a basis in graph theory for measuring completeness.
Cycle Graph (Cn)
A graph that consists of a single cycle, or a closed chain, of vertices. Significance: Models cyclic structures and problems.
Path Graph (Pn)
A graph that is a straightforward line of vertices in which each vertex is connected to exactly two other vertices, except for the endpoints. Significance: Represents the simplest form of a connected graph.
Wheel Graph (Wn)
Consists of a cycle with one additional central vertex that is connected to all other vertices. Significance: Models problems with a central hub and spokes.
Butterfly Graph
A specific 5-vertex graph that resembles a butterfly. Significance: Often used in parallel computing and network designs.
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