What is a unicursal graph?
Unicursal Graphs An open walk that includes (or traces) all edges of a graph without retracing any edge is called a unicursal line or open Euler line. A connected graph that has a unicursal line is called a unicursal graph.
What is meant 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 a traceable graph?
A traceable graph is a graph that possesses a Hamiltonian path. Hamiltonian graphs are therefore traceable, but the converse is not necessarily true.
What is the basic rule in Fleury’s algorithm?
Principle. The basic principle of Fleury’s algorithm is very simple. In order to find the Euler Path or Euler Circuit, the bridge edge should be the last edge we want to cross. This is because the bridge is the only edge connecting the two components of a graph.
How do you identify a Euler graph?
A graph has an Euler circuit if and only if the degree of every vertex is even. A graph has an Euler path if and only if there are at most two vertices with odd degree.
What is an Hamiltonian?
Definition of Hamiltonian : a function that is used to describe a dynamic system (such as the motion of a particle) in terms of components of momentum and coordinates of space and time and that is equal to the total energy of the system when time is not explicitly part of the function — compare lagrangian.
Can a graph be traced?
If a graph has no end vertices , you can ask the question: is it possible to trace over all the edges in the graph exactly once , without lifting your pencil? So, a graph is not traceable if it has more than two vertices of odd degree. …
What is the other name for a graph which is traceable?
Definitions. A Hamiltonian path or traceable path is a path that visits each vertex of the graph exactly once. A graph that contains a Hamiltonian path is called a traceable graph.
What is the difference between unicursal and Eulerian graphs?
In the terminology of the Wikipedia article, unicursal and eulerian both refer to graphs admitting closed walks, and graphs that admit open walks are called traversable or semi-eulerian. So I’ll avoid those terms in my answer.
What is the difference between open and closed unicursal tracing?
Obviously, a closed unicursal tracing of a line drawing is equivalent to an Euler circuit in the corresponding graph. Similarly, an open unicursal tracing equals to an Euler path. Thus, we end up with the following conditions: A line drawing has a closed unicursal tracing iff it has no points if intersection of odd degree.
What is the difference between directed and UN-directed graph?
Directed & Un-directed graph: If each edge of graph G has a direction then the graph is called Directed Graph (Example of directed graph fig.1). In Directed Graph each edge is represented by an arrow or direction curve from initial point u of e to the terminal point v (fig.2).
What is a regular graph?
A graph in which all vertices are of equal degree is called regular graph. The edges e2, e6 and e7 are incident with vertex v4. The edges e2 and e7 are adjacent. The edges e2 and e4 are not adjacent.