What is semi Eulerian graph?
A graph is semi-Eulerian if exactly two vertices have odd degree. Hamiltonian. Contains a Hamiltonian cycle – a closed path that includes all vertices, other than the start/end vertex, one time. Semi-Hamiltonian. Contains a semi-Hamiltonian path – an open path that includes all vertices once.
What do you mean by Eulerian graph?
An Eulerian cycle, Eulerian circuit or Euler tour in an undirected graph is a cycle that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal. The term “Eulerian graph” is also sometimes used in a weaker sense to denote a graph where every vertex has even degree.
What is the difference between Hamiltonian and semi-Hamiltonian?
A semi-Hamiltonian graph is a graph that contains a Hamiltonian path, but not a Hamilton cycle.
How do you know if a graph is semi Hamiltonian?
Like the graph 2 above, if a graph has a path that includes every vertex exactly once, but ending at another vertex than the starting one, then the graph is semi-Hamiltonian (is a semi-Hamiltonian graph).
What is Eulerian graph Theorem?
Theorem: An Eulerian trail exists in a connected graph if and only if there are either no odd vertices or two odd vertices. For the case of no odd vertices, the path can begin at any vertex and will end there; for the case of two odd vertices, the path must begin at one odd vertex and end at the other.
How can you tell if a graph is semi eulerian?
Semi-Euler Graph- If a connected graph contains an Euler trail but does not contain an Euler circuit, then such a graph is called as a semi-Euler graph. Graph must be connected. Graph must contain an Euler trail.
What does it mean if a graph is Hamiltonian?
A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices. A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph.
What is the difference between Hamiltonian graph and Euler graphs?
Important: An Eulerian circuit traverses every edge in a graph exactly once, but may repeat vertices, while a Hamiltonian circuit visits each vertex in a graph exactly once but may repeat edges.
