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Can a graph have an Euler circuit but not a Hamiltonian circuit?
JamesWinklergp5084
Yes.
An example:
_____A---------B________ A connected directly to B and D by one path.
_____|_______/|\________ B connected directly to A and E by one path, and to C by two paths.
_____|______/_|_\_______
_____|_____/___\_|______
_____|__E/_____\|______ E connected directly to B and D by one path.
_____|____\_____C______ C connected directly to B and D by two paths.
_____|_____\____|\_____
_____|______\___|__\___
_____|_______\__|__/___
_____|________\_|_/____
_____|_________\|/_____
_____-------------D_____ D connected directly to A and E by one path, and to C by two paths.
There is an Euler circuit: ABCDEBCDA
But a Hamiltonian circuit is impossible: as part of a circuit A can only be reached by the path BAD, but once BAD has been traversed it is impossible to get to both C and E without returning to B or D first. However there is a Hamiltonian Path: ABCDE.
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∙ 8y ago
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What is the difference between an Euler circuit and an Euler path?
The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.
What are Hamiltonian equations?
Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.
A circuit in a connected graph which includes every vertex of the graph is known?
Eular
What is Hamiltonian function?
The total energy of the system simply described in classical mechanics called as Hamiltonian.
Who calculated the value of e?
Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).
What is the difference between a Hamiltonian circuit and a Euler circuit?
In an Euler circuit we go through the whole circuit without picking the pencil up. In doing so, the edges can never be repeated but vertices may repeat. In a Hamiltonian circuit the vertices and edges both can not repeat. So Avery Hamiltonain circuit is also Eulerian but it is not necessary that every euler is also Hamiltonian.
What is the difference between an Euler circuit and an Euler path?
The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.
What is a hamiltonian path in a graph?
A path along the edges of a graph that traverses every vertex exactly once and terminates at its starting point. Also known as Hamiltonian circuit; Hamiltonian cycle.
Can a graph have a euler circuit but not a hamiltonian circuit?
Yes. Example: .................................................... ...A * ........................................... ......|.\ ......................................... eg Euler circuit: ACDCBA ......|...\ ........... --------- ............. ......|.....\........./...............\............ The Hamilton circuit is impossible as it has two ......|.......\...../...................\.......... halves (ACD & CD) connected to each other only ......|.........\./.......................\........ at vertex C. Once vertex C has been reached in ......|.......C *........................* D.... one half, it can only be used to start a path in ......|........./.\......................./......... the other half, or complete the cycle in the ......|......./.....\.................../........... current half; or if the path starts at C, it will end ......|...../.........\.............../............. without the other half being visited before C is ......|.../ ........... --------- .............. revisited. ......|./ ........................................... ...B *.............................................. ......................................................
What is a Euler path or circuit?
An euler path is when you start and one point and end at another in one sweep wirthout lifting you pen or pencil from the paper. An euler circuit is simiar to an euler path exept you must start and end in the same place you started.
What type of math is leonhard euler famous for?
Calculus and Graph Theory.
What are some of the accomplishments of Leonhard Euler?
Leonhard Euler is known as a Swiss mathematician and physicist. He made many famously known accomplishments in the area of calculus and graph theory.
What is a Hamiltonian Circuit?
a path that starts and ends at the same vertex and passes through all the other vertices exactly once...
What are Hamiltonian equations?
Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.
What is a circuit in graph theory?
no
What is the difference between NP and NP Complete problems?
- a problem in NP means that it can be solved in polynomial time with a non-deterministic turing machine - a problem that is NP-hard means that all problems in NP are "easier" than this problem - a problem that is NP-complete means that it is in NP and it is NP-hard example - Hamiltonian path in a graph: The problem is: given a graph as input, an algorithm must say whether there is a hamiltonian path in it or not. in NP: here is an algorithm that works in polynomial time on a non-deterministic turing machine: guess a path in the graph. Check that it is really a hamiltonian path. NP-hard: we use reduction from a problem that is NP-comlete (SAT for example). Given an input for the other problem we construct a graph for the hamiltonian-path problem. The graph should have a path iff the original problem should return "true". Therefore, if there is an algorithm that executes in polynomial time, we solve all the problems in NP in polynomial time.j
Did Leonhard Euler develop a type of math?
Euler made many contributions to virtually every area of math. His complete works fill a whole library shelf. You might say he invented graph theory.
