Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
In this unit we shall embark on the study of the algebraic object known as a group which serves as one of the fundamental building blocks for the subject today called abstract algebra.
Graphs - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit III: Graphs
An Euler circuit in a graph G is a simple circuit containing every edge of G.An Euler path in G is a simple path containing every degree of G.
Graphs - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit III: Graphs
A path in a multigraph G consists of an alternating sequence of vertices and edges of the form V0, e1 V1, e2, V2, … en-1, Vn-1, en, Vn
Graphs - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit III: Graphs
We can represent a simple graph in the form of edge list or in the form of adjacency lists which are may be useful in computer programming.
Graphs - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit III: Graphs
Two vertices u and v in an undirected graph G are called adjacent (or neighbors) in G if u, v are endpoints of an edge of G.If e is associated with (u, v), the edge e is called incident with the vertices u and v.
Graphs - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit III: Graphs
Graphs and graph models - Graph terminology and special types of graphs - Representing graphs and graph isomorphism - connectivity - Euler and Hamilton paths.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
Let X and Y be two finite subsets of a universal set U. If X and Y are disjoint, then |XUY| =│X│∩+ │Y│ If X and Y are not disjoint then |XUY| =│X | + | Y | - | X∩Y |. This is called the principle of inclusion and exclusion.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
The generating function for the sequence a0, a1, … ak, … of real numbers is the infinite series.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
Linear Recurrence Relation with constant coefficient. The three methods of solving recurrence relations are 1. Iteration, 2. Characteristic roots and 3. Generating functions.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
A recurrence relation for the sequence {an} is an equation that shows an in terms of one or more of the previous terms of the sequence a0, a1, ... an-1, for all integers n with n ≥ n0, where no is a non-negative integer.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
A permutation of a set of distinct objects is an ordered arrangement of these objects. A combination is a selection of objects without regard to order.
Combinatorics - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit II: Combinatorics
It states that if there are more pigeons (objects) than the pigeonholes (boxes), then some pigeonhole (box) must contain two or more pigeons (objects). The pigeohole principle is also called the Dirichlet drawer principle or Shoe box principle.