Standard ways of traversing a graph, Data Structure & Algorithms

Q. Which are the two standard ways of traversing a graph?  Explain them with an example of each. 

Ans:

 

The two ways of traversing a graph are written below

i. The depth-first traversal     of a graph is same as the depth-first traversal of a tree. Since a graph does not have any root, when we do a depth-first traversal, we must specify the vertex at which to begin. Depth-first traversal of a graph visits a vertex and then recursively visits all the vertices adjacent to that particular node. The catch is that the graph may have cycles, but the traversal must visit each and every vertex at most once. The solution to the trouble is to keep track of the nodes that have been visited, so that the traversal does not undergo the fate of infinite recursion.

ii. The breadth-first traversal     of a graph is same as the breadth-first traversal of the tree. Breadth-first tree traversal first of all visits all the nodes at the  depth zero (which is the root), then it visits all the nodes at depth one, and this process continues. Since a graph does not has root, when we perform a breadth-first traversal, we should specify the vertex at which to start the traversal. Furthermore, we can define the depth of the given vertex to be the length of the shortest path from the starting vertex to the vertex given to us.

Hence, breadth-first traversal first visits the beginning vertex, then all the vertices adjacent to the starting vertex, and the all the vertices adjacent to those, and it continues.

 

Posted Date: 7/10/2012 6:01:03 AM | Location : United States







Related Discussions:- Standard ways of traversing a graph, Assignment Help, Ask Question on Standard ways of traversing a graph, Get Answer, Expert's Help, Standard ways of traversing a graph Discussions

Write discussion on Standard ways of traversing a graph
Your posts are moderated
Related Questions
Binary Space Partition A binary space-partitioning (BSP) tree is an efficient method for determining object visibility by painting surfaces onto the screen from back to front,

A stack is a last in, first out (LIFO) abstract data type and sequential data structure. A stack may have any abstract data type as a component, but is characterized by two fundame

Define a sparse metrics. A matrix in which number of zero entries are much higher than the number of non zero entries is known as sparse matrix. The natural method of showing m

Graph terminologies : Adjacent vertices: Two vertices a & b are said to be adjacent if there is an edge connecting a & b. For instance, in given Figure, vertices 5 & 4 are adj

how to write an algorithm for unions & intersection of two linklists?

The below formula is used to calculate n: n = (x * x)/ (1 - x). Value x = 0 is used to stop the algorithm. Calculation is repeated using values of x until value x = 0 is input. The

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

Explain the representations of graph. The different ways of representing a graph is: Adjacency list representation : This representation of graph having of an array Adj of

A linear collection of data elements where the linear node is given by means of pointer is known as Linked list

Design  and implement  an algorithm  to simulate car  re-organizing of the train at the railway switching junction. You can only use stacks as the data structure to represent the t