RozgarDesh (रोजगार देश)

Eulerian circuit In this tutorial, We will learn about a special type of graph circuit called  Eulerian circuit Eulerian circuit A simple circuit is a walk where first and last point are the same and no edges are repeated. A Euler’s circuit is a simple circuit which uses all possible edges of the graph. The vertices can be repeated. The definition of Eulerian circuits arose from the problem of Konigsberg bridges Konigsberg Bridges Problem: There are four regions connected with seven bridges. Can you go through all the bridges without revisiting any bridge? Here in figure left side representing the Konigsberg bridges and right side figure is a theoretical representation of the bridge (edge) and cities (vertices). The question is equivalent to finding a Eulerian circuit in the graph. A connected graph (not necessarily simple) has a Eulerian circuit iff all vertices have even degree. Please write comments if you find any...

Trees In this tutorial, We will learn about the tree in graph theory. Tree A graph is called a tree if The graph is connected i.e  there are no unreachable vertices There are no cycles in the graph Example: Path graph is the simplest example of a tree Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Type of Graph In this tutorial, We will learn about some more variety of graph Simple Graph A graph is a simple graph, it is an unweighted, undirected and containing no graph loops or multiple edges Multigraph In graph theory, a multigraph is a graph which is permitted to have multiple edges Isomorphic Graph Two graphs having the same number of vertices, edges, and also the same edge connectivity but different forms are called an isomorphic graph. Subgraph A subgraph is a graph whose vertices and edges form subsets of the graph vertices and graph edges of a given graph. All the edges and vertices of the graph might not be present in subgraph; but if a vertex is present in the subgraph, it has a corresponding vertex in the graph and any edge that connects two vertices in subgraph will also connect the corresponding vertices in the graph. All graphs are subgraphs of itself. Degree of Graph The degree of a vertex of a graph is the number of edges incident to the...

Graph Connectivity In this tutorial, We will learn about the term path, walk and cycle that used in the connectivity. The connectivity means how the graph vertices are connected to each other like Given a graph, can we reach from a source vertex s to target vertex t using the edges of the graph? Walk in Graph A walk in a graph is a sequence of vertices where any two consecutive vertices are by an edge. In a walk, it is allowed to take vertices multiple times. The length of the walk is the number of the edge in the walk. Path in Graph If all the vertices in a walk are distinct, except possibly the first and the last vertex, then it is called a path. Cycle in Graph A path of length greater than two is called a cycle if the first and the last vertex are the same. Loop in Graph A loop in is an edge that connects a vertex to itself. Multi-edge in Graph Multiple edges(also called parallel edges) are two or more edges that are incident to the same two ver...

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Graph Theory In this tutorial, We will learn about the basic terms and their definitions that widely used in the field of graph theory. Introduction Graph theory is a branch of mathematics and computer science where we study mathematical structure which used to model the relationship between objects. Here the structure is a graph, objects are nodes or vertex and relation that join any two objects called node.   In the given figure Graph : Whole structure (A, B, C, D, E, F) and all lines Node/Vertex : A, B, C, D, E, and F are vertex Edge : The line joining any two vertexes is edge Example: AB, AC, AD, BC, BE, DE, and DF are edge Undirected Graph An undirected graph is a set of objects (called vertices or nodes) that are connected together, where all the edges are bidirectional. Directed Graph A directed graph is a set of objects (called vertices or nodes) that are connected together, where all the edges are directed from one vertex to another. Unw...

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