In discrete mathematics, the difference between simple and elementary loops.

First, the reference is different.

1. Simple loop: In the vertex sequence of the graph, except for the first vertex and the last vertex are the same, the rest of the vertices do not repeat the loop.

2. Primary circuit: Add any one connecting branch to the tree, and you can form a loop with the remaining several tree branches, so as to contain and only contain one connected branch.

Second, the characteristics are different.

1. Simple loop: The path or loop does not contain the same edges repeatedly.

2. Primary loop: A path in the diagram includes each edge exactly once.

Third, the traversal method is different.

1. Simple loop: start from a certain node, and then find out a loop path that starts from this and returns to this point. This approach does not guarantee that every edge will be traversed.

If the edge of a point is not traversed, let that point be the starting point, and this edge is the starting edge, and connect it to the current loop. This is done until all edges are traversed.

2. Primary loop: each node has zero or more sub-nodes; A node that does not have a parent node is called a root node; Each non-root node has one and only one parent; In addition to the root node, each child node can be divided into multiple disjoint subtrees. In a connectivity diagram, the branches that make up the tree are called branches, and the rest of the branches are called branches.

The intuitive meaning of the road is to start from the first node, follow the edge associated with it to (enter) the second node, and then follow the edge associated with the second node (exit the second node, enter) the third node, and so on until it stops at a certain node. This results in a road that starts at the first node and ends at the last node.

In a road, if the edges are all different, the road is said to be primary, and if the nodes are not the same, the road is called the basic road. If the above two conditions are not met, it is called an easy road.

If the end point is the same as the starting point, that is, the end is the end and back to the starting point, so that the result is a loop. In a loop, if the edges are not the same, the circuit is called the primary loop, if the nodes are not the same (except that the starting point and the end point can be the same), the circuit is called the basic loop, and if the above two conditions are not met, it is called a simple loop.

That's what you asked. It doesn't make sense if it's a simple or basic pathway, or an Euler or Hamiltonian pathway. If any graph exists in a ring, there are infinite pathways. There are no loops in a particular directed graph, and that's the tree. Do you think it still makes sense? Waiting for you to modify the question.

The primary pathway must be the simple pathway.

The simple pathway is not necessarily the primary pathway.

Yes. In discrete mathematics, when the end point and the beginning point of a path coincide, it is called a loop, so a loop belongs to a path.

Given the graph g = (undirected or directed graph), the alternating sequence of vertices and edges in g =v0e1v1e2?envn.where 1<=i<=n,ei=(vi-1,vi), is called the V0 to VN pathway.

v0 and vn are the start and end points of the pathway, respectively, and n (the number of edges) is the length of the path.

1. Refer to different simple loops: In the vertex sequence of the graph, except for the first vertex and the last vertex are the same, the rest of the vertices do not repeat the loop. Primary Loop:

If you add any one branch to the tree, you can form a loop with the remaining branches, so that it contains and only one loop. 2. Simple loops with different characteristics: paths or loops do not contain the same edges repeatedly.

Primary loop: A path in the diagram encompasses each edge exactly once.

The difference between the simple path and the primary pathway starvation:

1. The primary pathway must be a simple pathway, and the simple pathway is not necessarily a primary pathway.

2. The primary path is that each node only passes once, and the simple path is that the edge only passes once. Rotten wisdom is blind.

3. If all the edges in the path are different from each other, it is called a simple path or trace.

If all the nodes in the path are different from each other and all the edges are different from each other, it is called the basic path or primary path or path.

The difference can be seen from their definitions: Euler pathway refers to a ...... through each edge, while the Hamiltonian pathway is ...... through each vertex once

The path requires that the nodes in the loop are not repeated, and the loop only needs to coincide with the initial point of the end point, and if the nodes in the loop are not repeated, it belongs to the path.

The loop is a special case of the path:

A loop is a path where the start and end points coincide.

Yes the loop must be the pathway, and the loop is the special case of the pathway.