There are various types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure. We will discuss only a certain few important types of graphs in this chapter.Null GraphA graph having no edges is called a Null Graph.ExampleIn the above graph, there are three ... Read More

The inverse of a one-to-one corresponding function f: A → B, is the function g: B → A, holding the following property −f(x) = y ⇔ g(y) = xThe function f is called invertible if its inverse function g exists.ExampleA Function f : Z → Z, f(x)=x+5, is invertible since ... Read More

Graph traversal is the problem of visiting all the vertices of a graph in some systematic order. There are mainly two ways to traverse a graph.Breadth First SearchDepth First SearchDepth First Search (DFS) algorithm starts from a vertex v, then it traverses to its adjacent vertex (say x) that has ... Read More

Two graphs G1 and G2 are said to be homomorphic, if each of these graphs can be obtained from the same graph 'G' by dividing some edges of G with more vertices. Take a look at the following example −Divide the edge 'rs' into two edges by adding one vertex.The ... Read More

Graphs come with various properties which are used for characterization of graphs depending on their structures. These properties are defined in specific terms pertaining to the domain of graph theory. In this chapter, we will discuss a few basic properties that are common in all graphs.Radius of a Connected GraphThe ... Read More

A graph is a diagram of points and lines connected to the points. It has at least one line joining a set of two vertices with no vertex connecting itself. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree ... Read More

Euler Graph - A connected graph G is called an Euler graph, if there is a closed trail which includes every edge of the graph G.Euler Path - An Euler path is a path that uses every edge of a graph exactly once. An Euler path starts and ends at ... Read More

Cardinality of a set S, denoted by |S|, is the number of elements of the set. The number is also referred as the cardinal number. If a set has an infinite number of elements, its cardinality is ∞.Example − |{1, 4, 3, 5}| = 4, |{1, 2, 3, 4, 5, ... Read More

A Function assigns to each element of a set, exactly one element of a related set. Functions find their application in various fields like representation of the computational complexity of algorithms, counting objects, study of sequences and strings, to name a few. The third and final chapter of this part ... Read More

Problem StatementFind the number of spanning trees in the following graph.SolutionThe number of spanning trees obtained from the above graph is 3. They are as follows −These three are the spanning trees for the given graphs. Here the graphs I and II are isomorphic to each other. Clearly, the number ... Read More