Graphs for GATE CS

By : Manglika Tripathi

Updated : Feb 26, 2021, 16:48

Graphs are terms used to describe multiple vertices connected through a combination of edges. The study of these graphs is known as graph theory. It is an essential topic in many engineering competitive examinations. In layman's terms, graphs are a combination of vertices and edges. Generally, many diagram-based questions are asked from the sub-topics and types related to graphs. This article will tell you where to go for graphs study material for GATE CS, graphs GATE questions and answers pdf, graphs online quizzes, graphs topics for GATE CS, graphs notes for GATE pdf, and graphs online tests. It will provide a comprehensive overview of the topic to prepare for the GATE CS.

Important Graphs Topics for GATE CS



Null graphs

Graphs that have vertices, but do not have any edges are called null graphs.

Konigsberg bridge problem

Konigsberg problem states that "Is it possible to cross four areas (A, B, C, D) using seven bridges without swimming in the river exactly once and arriving back from where you started"

Handshaking theorem

The handshaking theorem states the following conclusions:

  • The addition of the degrees of all the vertices in the graph is even.
  • The addition of odd degree vertices is even.
  • The number of odd degree vertices in the graph is always even.

This theorem is also known as the Sum of degree theorem.

Isomorphic graphs

Any two graphs are said to be isomorphic if they fulfil the following conditions:

  • Vertices in both graphs are the same.
  • Edges in both the graphs are the same.
  • The degrees of the vertices are equal in both the graphs.
  • The cycle of length formed in any one graph must be similar to the cycle of the other graph’s length.

Graph colouring

Graph colouring is the process of colouring the graph’s vertices such that every vertex is assigned some different colour. It is also known as vertex colouring and graph so formed is known as a properly coloured graph.

Graph complement

The complement of graph A is a graph A' such that A' has all vertices of graph A and A' with edges that do not exist in A.

Tips to Solve Graphs Questions in GATE CS Exam

Following are some tips to keep in mind while preparing for questions on graphs:

  • There are many diagrams, types, and theorems involved in graphs, so practice as much as possible to solve questions faster in the examination.
  • It is one of the highest-scoring components of GATE examinations, so practising it properly will definitely help in scoring well.
  • The weightage of graphs topics is really high in the GATE CS examination, so do not leave out any subtopic or portion from this topic, especially.
  • Practice with diagrams, especially in theorem questions to help you understand problems easily and score well.

Importance of Graphs in the GATE Exam

Here's why graphs form an essential part of GATE:

  • Graphs are one of the most important components of engineering examinations, as every year, these examinations include a lot of questions on topics related to graphs.
  • The weightage of graphs in the GATE CS examination is one of the highest, but it is still the easiest component of GATE, so practising it will help you score well.
  • Around two to three questions are asked every year on topics related to graphs in the GATE CS.
  • Graphs are tested for around 5 marks in GATE examination, so it is important to score well.

Most Recommended Books for Graphs for GATE

There are many books to prepare for graphs and related topics for the GATE CS examinations, so you have to choose wisely. The below list of graph books for GATE will help you understand the possible graphs GATE questions.



Graphs theory

Narsingh Deo

Graph theory with applications

John Adrian Bondy

Introduction to Graph Theory

Richard J Trudeau

Why prepare graphs from BYJU'S Exam Prep?

Gradeup is an online platform that allows students to interact, communicate, and address their queries. It provides students with an environment to study using high-quality, verified examination material and practice previous years' examination papers, too. It gives students access to preparation material, which boosts aspirants' confidence. It also provides students with mock tests to practice examinations. It even conducts regular live sessions to clarify students' doubts. You can also find graphs quizzes, graphs, GATE notes, and graphs GATE syllabus to prepare for examinations at BYJU'S Exam Prep.

Frequently Asked Questions

Q. What is the weightage of graphs questions in competitive examinations?

On average, around 2-3 questions are asked on graphs, types and related topics in competitive examinations.

Q. What is the updated graphs syllabus for GATE CS?

You can find the updated graphs syllabus for GATE and graphs notes for CS on the BYJU'S Exam Prep website.

Q. How are questions related to Graphs asked in competitive examinations?

They are usually asked in the form of theoretical and diagram-based MCQs. You can prepare accordingly with the graphs MCQ questions and graphs MCQ pdf compiled by BYJU'S Exam Prep.

Q. What is the difficulty level of graphs questions in examinations?

The difficulty level of these questions is not too high, so you can easily solve them and score well in examinations.

Q. What are the applications of graphs in computer science?

Graphs for GATE computer science is usually used to study the following theorems and algorithms:

  • Kruskal's algorithm
  • Prim's algorithm
  • Dijkstra's algorithm