Some Basic Theorems on Trees

Tree:- A connected graph without any circuit is called a Tree. In other words, a tree is an undirected graph G that satisfies any of… Read More »

Basic Properties of a Graph

A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are… Read More »

Degree of a Cycle Graph

Given the number of vertices in a Cycle Graph. The task is to find the Degree and the number of Edges of the cycle graph.… Read More »

Program to find the diameter, cycles and edges of a Wheel Graph

Wheel Graph: A Wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. Properties:- Wheel graphs are… Read More »

Vizing’s Theorem

In graph theory, Vizing’s theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one… Read More »

Remove all outgoing edges except edge with minimum weight

Given a directed graph having n nodes. For each node, delete all the outgoing edges except the outgoing edge with minimum weight. Apply this deletion… Read More »

Data Structures | Graph | Question 9

Given an undirected graph G with V vertices and E edges, the sum of the degrees of all vertices is (A) E (B) 2E (C)… Read More »

Data Structures | Graph | Question 8

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the… Read More »

Data Structures | Graph | Question 9

Which of the following statements is/are TRUE for an undirected graph? P: Number of odd degree vertices is even Q: Sum of degrees of all… Read More »

Data Structures | Graph | Question 6

How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ?… Read More »

Data Structures | Graph | Question 5

Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v)… Read More »

Data Structures | Graph | Question 4

The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity. (A)… Read More »

Data Structures | Graph | Question 3

The time complexity of computing the transitive closure of a binary relation on a set of n elements is known to be: (A) O(n) (B)… Read More »

Data Structures | Graph | Question 2

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the… Read More »

Data Structures | Graph | Question 1

Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? (A) In adjacency list representation, space is… Read More »