## Proof that vertex cover is NP complete

Prerequisite – Vertex Cover Problem, NP-Completeness Problem – Given a graph G(V, E) and a positive integer k, the problem is to find whether there… Read More »

## Graph measurements: length, distance, diameter, eccentricity, radius, center

Prerequisite – Graph Theory Basics – Set 1, Set 2 A graph is defined as set of points known as ‘Vertices’ and line joining these… Read More »

## Mathematics | Law of total probability

Prerequisite – Random variables, Conditional probability Given n mutually exclusive events A1, A2, …Ak such that their probabilities sum is unity and their union is… Read More »

## Discrete Mathematics | Hasse Diagrams

A Hasse diagram is a graphical representation of the relation of elements of a partially ordered set (poset) with an implied upward orientation. A point… Read More »

## Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph

Prerequisite – Graph Theory Basics – Set 1 1. Walk – A walk is a sequence of vertices and edges of a graph i.e. if… Read More »

## Inverse functions and composition of functions

Inverse Functions – In mathematics a function, a, is said to be an inverse of another, b, if given the output of b a returns… Read More »

## Placement | Cubes

A type of cuboid in which all the sides i.e length, breadth & height are equal. All faces of cubes are of the same area.… Read More »

## Mathematics | Introduction to Proofs

Mathematical proof is an argument we give logically to validate a mathematical statement. In order to validate a statement, we consider two things: A statement… Read More »

## Mathematics | Probability

Probability refers to the extent of occurrence of events. When an event occurs like throwing a ball, picking a card from deck, etc ., then… Read More »

## Scales of Measurement

Data can be classified as being on one of four scales: nominal, ordinal, interval or ratio. Each level of measurement has some important properties that… Read More »

## Mathematics | Independent Sets, Covering and Matching

1. Independent Sets – A set of vertices I is called independent set if no two vertices in set I are adjacent to each other… Read More »

## Mathematics | Sequence, Series and Summations

SEQUENCE: It is a set of numbers in a definite order according to some definite rule (or rules). Each number of the set is called… Read More »

## Mathematics | Covariance and Correlation

Covariance and Correlation are two mathematical concepts which are commonly used in the field of probability and statistics. Both concepts describe the relationship between two… Read More »

## Discrete Mathematics | Representing Relations

Prerequisite – Introduction and types of Relations Relations are represented using ordered pairs, matrix and digraphs: Ordered Pairs – In this set of ordered pairs… Read More »

## Discrete Mathematics | Types of Recurrence Relations – Set 2

Prerequisite – Solving Recurrences, Different types of recurrence relations and their solutions, Practice Set for Recurrence Relations The sequence which is defined by indicating a… Read More »