Graph Theory | BCS405B | Model Question Paper + Important Questions With Solutions (EXPLAINED) | CSE Stream | 2022 Scheme | Video Course And Study Material

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Enrollment Expiration: 60 days
Duration: 2 hours

Very Important Questions with solutions explained (Last Moment Exam Preparation Course )

Graph Theory || BCS405B || Model Question Paper + Important Questions with Solutions (EXPLAINED) || CSE Stream || 2022 Scheme || Video Course and Study Material

Get ready for your VTU 4th semester exams quickly and effectively with our Last Moment Exam Preparation Course. This course is designed to help you do your best by focusing on the most important parts of your syllabus.

Course Highlights for Graph Theory (BCS405B):

Model Paper with Solutions : Get a model paper for Graph Theory with complete solutions, similar to your actual exams. Many of the questions on your exam may be like the ones in this model paper.
Very important questions module wise explained : Get a Very important questions module wise explained in video course for Graph Theory, similar to your actual exams. Many of the questions on your exam may be like the ones in this course.
Downloadable Study Materials: Instantly access high-quality, downloadable study materials. These resources give you clear, focused information to make your study time more efficient.
Focused Content: This course is perfect for last-minute preparation, helping you cover all the important topics and concepts quickly for Graph Theory (BCS405B).
Certificate: You will also get a certificate on course completion.

Whether you’re a current VTU 4th semester student or have backlogs to clear, go into your exams with confidence, knowing you are well-prepared. Sign up now and give yourself the best chance to succeed!

Course Content

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Module-1

1] Define sub graph and pendent vertex with example

06:30
2] consider the following graph G (1).what type of a graph is G (2).find the pendent vertices in G (3). How many components are there in G ? (4). Find the minimum degree d(G) (5). Find the average degree d(G) (6).Draw two vertex disjoint sub-graph of G.

08:21
3] Show that the number of vertices of odd degree in a graph is always even.

05:30
4] Show that the maximum number of edges in a simple graph with n vertices is n(n – 1)/2 .

04:31
5] Distinguish between Complete graph and Complete Bipartite graph.

03:48
6] Verify whether the following graphs are isomorphic or not.

08:59
7] Determine whether the following graphs are isomorphic (or) not

04:40
8] Define Walk and their classification with example

08:00

Module-2

Module-3

1] Prove that a connected graph G is a tree if and only if there is one and only one path between every pair of vertices

06:40
2] Show that a tree with n vertices has n − 1 edges.

06:01
3] Prove that there are atleast two pendent vertices in a tree with or more vertices

07:13
4] Define spanning tree. show that Every connected graph contains a spanning tree

09:10
5] Find the number of tree branches and chords in the following graph with 7 vertices and 14 edges.

04:17
6] Define Fundamental Circuit. If G is a graph with n vertices and q edges, then find the number of fundamental circuits in the graph.

10:22
7] Define Vertex connectivity and Edge connectivity, cut-set and fundamental cut-set

06:19

Module-4

Module-5

1] Prove that ever tree with two or more vertices is 2-chromatic

10:16
2] Define chromatic number .Prove that a graph with atleast one edge is 2-chromatic if and if it has no circuit of odd length

09:32
3] Define chromatic polynomial and write the chromatic polynomial of a graph with n vertices

06:03
4] Find the chromatic polynomial of the given graph and also chromatic number

09:43
5] Define Matching and complete matching. Obtain two complete matching from the given graph.

11:05
6] Define Covering and minimal covering of a graph. Obtain two minimal coverings from the given graph.

03:16
7] Prove that an n -vertex graph is a tree if and only if its chromatic polynomial is Pn (λ) = λ(λ − 1)n−1 .

05:27
8] State and prove Five color theorem.

02:44

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About Course

Very Important Questions with solutions explained (Last Moment Exam Preparation Course )

Course Highlights for Graph Theory (BCS405B):

What Will You Learn?

Course Content

How to watch video course and download study material from enrolled courses?

How to watch video courses?

How to download Study Materials (PDF) from the enrolled courses?

Module-1

1] Define sub graph and pendent vertex with example

2] consider the following graph G (1).what type of a graph is G (2).find the pendent vertices in G (3). How many components are there in G ? (4). Find the minimum degree d(G) (5). Find the average degree d(G) (6).Draw two vertex disjoint sub-graph of G.

3] Show that the number of vertices of odd degree in a graph is always even.

4] Show that the maximum number of edges in a simple graph with n vertices is n(n – 1)/2 .

5] Distinguish between Complete graph and Complete Bipartite graph.

6] Verify whether the following graphs are isomorphic or not.

7] Determine whether the following graphs are isomorphic (or) not

8] Define Walk and their classification with example

Module-2

1] By specifying the walk, draw two Euler graphs and an Unicursal graph.

2] If all the vertices in a connected graph G are of even degree, then show that G is Eulerian.

3] Define Hamiltonian cycle. How many edge-disjoint Hamiltonian cycles exist in a complete graph with 5 vertices? Draw the graph to show and specify the cycle.

4] Draw the Graph that has a Hamiltonian path put does not have a Hamiltonian circuit.

5] prove that in the complete graph with n vertices where n is an odd number and greater than (or) equal to 3 then there are (n-1)/2 edge disjoint Hamilton cycle.

Module-3

1] Prove that a connected graph G is a tree if and only if there is one and only one path between every pair of vertices

2] Show that a tree with n vertices has n − 1 edges.

3] Prove that there are atleast two pendent vertices in a tree with or more vertices

4] Define spanning tree. show that Every connected graph contains a spanning tree

5] Find the number of tree branches and chords in the following graph with 7 vertices and 14 edges.

6] Define Fundamental Circuit. If G is a graph with n vertices and q edges, then find the number of fundamental circuits in the graph.

7] Define Vertex connectivity and Edge connectivity, cut-set and fundamental cut-set

Module-4

1] State and prove Euler’s formula that gives the number of regions in any planar graph

2] Define planar and non-planar graphs. State Kuratowski’s theorem. Draw Kuratowski’s two graphs.

3] If G is a simple planar Graph with atleast three vertices then show that

4] Prove that planar Graph contains a vertex of degree atmost 5

5] Draw the Geometric Dual of the given graph

Module-5

1] Prove that ever tree with two or more vertices is 2-chromatic

2] Define chromatic number .Prove that a graph with atleast one edge is 2-chromatic if and if it has no circuit of odd length

3] Define chromatic polynomial and write the chromatic polynomial of a graph with n vertices

4] Find the chromatic polynomial of the given graph and also chromatic number

5] Define Matching and complete matching. Obtain two complete matching from the given graph.

6] Define Covering and minimal covering of a graph. Obtain two minimal coverings from the given graph.

7] Prove that an n -vertex graph is a tree if and only if its chromatic polynomial is Pn (λ) = λ(λ − 1)n−1 .

8] State and prove Five color theorem.

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