There are mainly two ways to represent a graph −Adjacency MatrixAdjacency ListAdjacency MatrixAn Adjacency Matrix A[V][V] is a 2D array of size V × V where $V$ is the number of vertices in a undirected graph. If there is an edge between Vx to Vy then the value of A[Vx][Vy]=1 ... Read More

Relations may exist between objects of the same set or between objects of two or more sets.Definition and PropertiesA binary relation R from set x to y (written as xRy or R(x, y)) is a subset of the Cartesian product x × y. If the ordered pair of G is ... Read More

Predicate Calculus deals with predicates, which are propositions containing variables.PredicateA predicate is an expression of one or more variables defined on some specific domain. A predicate with variables can be made a proposition by either assigning a value to the variable or by quantifying the variable.Consider the following statement.Ram is ... Read More

Power set of a set S is the set of all subsets of S including the empty set. The cardinality of a power set of a set S of cardinality n is 2n. Power set is denoted as P(S).Example −For a set S = { a, b, c, d } ... Read More

Planar graph − A graph G is called a planar graph if it can be drawn in a plane without any edges crossed. If we draw graph in the plane without edge crossing, it is called embedding the graph in the plane.Non-planar graph − A graph is non-planar if it ... Read More

A graph 'G' is said to be planar if it can be drawn on a plane or a sphere so that no two edges cross each other at a non-vertex point.ExampleRegionsEvery planar graph divides the plane into connected areas called regions.ExampleDegree of a bounded region r = deg(r) = Number ... Read More

Pendent VertexBy using degree of a vertex, we have a two special types of vertices. A vertex with degree one is called a pendent vertex.ExampleHere, in this example, vertex 'a' and vertex 'b' have a connected edge 'ab'. So with respect to the vertex 'a', there is only one edge ... Read More

Partition of a set, say S, is a collection of n disjoint subsets, say P1, P1, ... Pn that satisfies the following three conditions −Pi does not contain the empty set.                        [ Pi ≠ { ∅ } for all ... Read More

A spanning tree with assigned weight less than or equal to the weight of every possible spanning tree of a weighted, connected and undirected graph $G$, it is called minimum spanning tree (MST). The weight of a spanning tree is the sum of all the weights assigned to each edge ... Read More

A graph can be represented using Adjacency Matrix way.Adjacency MatrixAn Adjacency Matrix A[V][V] is a 2D array of size V × V where $V$ is the number of vertices in a undirected graph. If there is an edge between Vx to Vy then the value of A[Vx][Vy]=1 and A[Vy][Vx]=1, otherwise ... Read More