Mathematics can be broadly classified into two categories −Continuous Mathematics − It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. For example, a function in continuous mathematics can ... Read More

TautologiesA Tautology is a formula which is always true for every value of its propositional variables.Example − Prove [ (A → B) ∧ A ] → B is a tautologyThe truth table is as follows −ABA → B(A → B) ∧ A[ (A → B) ∧ A ] → BTrueTrueTrueTrueTrueTrueFalseFalseFalseTrueFalseTrueTrueFalseTrueFalseFalseTrueFalseTrueAs ... Read More

A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.Generally there are five connectives which are −OR (∨)AND (∧)Negation/ NOT (¬)Implication / ... Read More

A matching graph is a subgraph of a graph where there are no edges adjacent to each other. Simply, there should not be any common vertex between any two edges.MatchingLet 'G' = (V, E) be a graph. A subgraph is called a matching M(G), if each vertex of G is ... Read More

A covering graph is a subgraph which contains either all the vertices or all the edges corresponding to some other graph. A subgraph which contains all the vertices is called a line/edge covering. A subgraph which contains all the edges is called a vertex covering.Line CoveringLet G = (V, E) ... Read More

Kirchoff's theorem is useful in finding the number of spanning trees that can be formed from a connected graph.ExampleThe matrix 'A' be filled as, if there is an edge between two vertices, then it should be given as '1', else '0'.

IsomorphismIf two graphs G and H contain the same number of vertices connected in the same way, they are called isomorphic graphs (denoted by G ≅ H).It is easier to check non-isomorphism than isomorphism. If any of these following conditions occurs, then two graphs are non-isomorphic −The number of connected ... Read More

A graph can exist in different forms having the same number of vertices, edges, and also the same edge connectivity. Such graphs are called isomorphic graphs. Note that we label the graphs in this chapter mainly for the purpose of referring to them and recognizing them from one another.Isomorphic GraphsTwo ... Read More

Tree is a discrete structure that represents hierarchical relationships between individual elements or nodes. A tree in which a parent has no more than two children is called a binary tree.Tree and its PropertiesDefinition − A Tree is a connected acyclic undirected graph. There is a unique path between every ... Read More

Hamiltonian graph - A connected graph G is called Hamiltonian graph if there is a cycle which includes every vertex of G and the cycle is called Hamiltonian cycle. Hamiltonian walk in graph G is a walk that passes through each vertex exactly once.Dirac's Theorem - If G is a ... Read More