Article Categories
- All Categories
-
Data Structure
-
Networking
-
RDBMS
-
Operating System
-
Java
-
MS Excel
-
iOS
-
HTML
-
CSS
-
Android
-
Python
-
C Programming
-
C++
-
C#
-
MongoDB
-
MySQL
-
Javascript
-
PHP
Articles by Mahesh Parahar
Page 13 of 14
Finding the matching number of a graph
Problem StatementWhat is the matching number for the following graph?SolutionNumber of vertices = 9We can match only 8 vertices.Matching number is 4.
Read MoreFinding the line covering number of a graph
Problem StatementWhat is the line covering number for the following graph?SolutionNumber of vertices = |V| = n = 7Line covering number = (α1) ≥ ⌈ n / 2 ⌉ = 3α1 ≥ 3By using 3 edges, we can cover all the vertices.Hence, the line covering number is 3.
Read MoreFinding the chromatic number of complete graph
Problem StatementWhat is the chromatic number of complete graph Kn?SolutionIn a complete graph, each vertex is adjacent to is remaining (n–1) vertices. Hence, each vertex requires a new color. Hence the chromatic number Kn = n.
Read MoreEdges and Vertices of Graph
A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.Graph TheoryDefinition − A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. A vertex a represents an endpoint of an edge. An edge joins two vertices a, b and is represented by set of vertices it connects.Example − Let us ...
Read MoreDistance between Vertices and Eccentricity
Distance between Two VerticesIt is number of edges in a shortest path between Vertex U and Vertex V. If there are multiple paths connecting two vertices, then the shortest path is considered as the distance between the two vertices.Notation − d(U, V)There can be any number of paths present from one vertex to other. Among those, you need to choose only the shortest one.ExampleTake a look at the following graph −Here, the distance from vertex 'd' to vertex 'e' or simply 'de' is 1 as there is one edge between them. There are many paths from vertex 'd' to vertex ...
Read MoreConnectivity of Graph
Whether it is possible to traverse a graph from one vertex to another is determined by how a graph is connected. Connectivity is a basic concept in Graph Theory. Connectivity defines whether a graph is connected or disconnected. It has subtopics based on edge and vertex, known as edge connectivity and vertex connectivity. Let us discuss them in detail.ConnectivityA graph is said to be connected if there is a path between every pair of vertex. From every vertex to any other vertex, there should be some path to traverse. That is called the connectivity of a graph. A graph with ...
Read MoreConnected vs Disconnected Graphs
Connected GraphA graph is connected if any two vertices of the graph are connected by a path.Vertex 1Vertex 2PATHaba baca b c, a cada b c d, a c dbcb a c , b ccdc dDisconnected GraphA graph is disconnected if at least two vertices of the graph are not connected by a path. If a graph G is disconnected, then every maximal connected subgraph of G is called a connected component of the graph G.Vertex 1Vertex 2PATHaba bacNot AvailableadNot AvailablebcNot Availablecdc d
Read MoreComposition of Functions of Set
Two functions f: A → B and g: B → C can be composed to give a composition g o f. This is a function from A to C defined by (g o f)(x) = g(f(x))ExampleLet f(x) = x + 2 and g(x) = 2x + 1, find (f o g)(x) and (g o f)(x).Solution(f o g)(x) = f(g(x)) = f(2x + 1) = 2x + 1 + 2 = 2x + 3(g o f)(x) = g (f(x)) = g(x + 2) = 2 (x+2) + 1 = 2x + 5Hence, (f o g)(x) ≠ (g o f)(x)Some Facts about ...
Read MoreIntroduction to Mathematical Logic!\\n
The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like design of computing machines, artificial intelligence, definition of data structures for programming languages etc.Major CategoriesMathematical logics can be broadly categorized into three categories.Propositional Logic − Propositional Logic is concerned with statements to which the truth values, "true" and "false", can be assigned. The purpose is to analyse these statements either individually or in a composite manner.Predicate ...
Read MoreComplement of Graph
Let 'G−' be a simple graph with some vertices as that of 'G' and an edge {U, V} is present in 'G−', if the edge is not present in G. It means, two vertices are adjacent in 'G−' if the two vertices are not adjacent in G.If the edges that exist in graph I are absent in another graph II, and if both graph I and graph II are combined together to form a complete graph, then graph I and graph II are called complements of each other.ExampleIn the following example, graph-I has two edges 'cd' and 'bd'. Its complement ...
Read More