What is a hamiltonian path in a graph?

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

Can a graph have an Euler circuit but not a Hamiltonian circuit?

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.

What touches every vertex exacaly once but does not return to its origin?

Hamiltonian path

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.

When does a directed acyclic graph yield a unique topological sort?

Understanding when a Directed Acyclic Graph (DAG) yields a unique topological sort is an intriguing aspect of graph theory and algorithms. A Directed Acyclic Graph is a graph with directed edges and no cycles. Topological sorting for a DAG is a linear ordering of vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. A unique topological sort in a DAG occurs under a specific condition: when the graph has a unique way to visit its vertices without violating the edge directions. This is possible only if the graph has a unique Hamiltonian path, meaning there is a single path that visits every vertex exactly once. To determine if a DAG has a unique topological sort, you can check for the presence of a Hamiltonian path. One approach to do this is using the concept of in-degree and out-degree of vertices (the number of incoming and outgoing edges, respectively). For a DAG to have a unique topological sort, each vertex except one must have an out-degree of exactly one. Similarly, each vertex except one must have an in-degree of exactly one. The starting vertex of the Hamiltonian path will have an out-degree of one and in-degree of zero, and the ending vertex will have an out-degree of zero and in-degree of one. If these conditions are met, the DAG will have a unique topological sort. In practical applications, this concept is significant in scenarios where tasks need to be performed in a specific order. For example, in project scheduling or course prerequisite planning, knowing whether a DAG has a unique topological sort can help in determining if there is only one way to schedule tasks or plan courses. In summary, a Directed Acyclic Graph yields a unique topological sort if and only if it contains a unique Hamiltonian path. This scenario is characterized by each vertex (except for the start and end) having exactly one in-degree and one out-degree. Understanding this concept is crucial in areas like scheduling and planning, where order and precedence are key.

What is the perimeter o a 10 by 10 6 sided cube?

A cube has 12 edges so 120 but a Hamiltonian path doesn't appear to be possible.

What is the proper adjective for Hamilton?

Hamiltonian is the proper adjective for Hamilton. For instance: The Hamiltonian view on the structure of government was much different from that of Jefferson.

What is Hamiltonian function?

The total energy of the system simply described in classical mechanics called as Hamiltonian.

What rhymes with dath?

math, calf, path, laughed, graph

What is Chrono cycle graph?

Similar to cycle graph except that along with path it also shows direction and speed of movement.

C plus plus program for hamiltonian cycle algo?

#include #include #include #include using namespace std;vector procedure_1(vector< vector > graph, vector path);vector procedure_2(vector< vector > graph, vector path);vector procedure_2b(vector< vector > graph, vector path);vector procedure_2c(vector< vector > graph, vector path);vector procedure_3(vector< vector > graph, vector path);vector sort(vector graph);vectorreindex(vector graph, vector index);ifstream infile ("graph.txt"); //Input fileofstream outfile("paths.txt"); //Output fileint main(){int i, j, k, n, vertex, edge;infile>>n; //Read number of verticesvector< vector > graph; //Read adjacency matrix of graphfor(i=0; iedge;row.push_back(edge);}graph.push_back(row);}vector index=sort(graph);graph=reindex(graph,index);for(vertex=0; vertex

What is a hamiltonian path in a graph?

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