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Module-1
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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.
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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
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1] By specifying the walk, draw two Euler graphs and an Unicursal graph.
13:31
2] If all the vertices in a connected graph G are of even degree, then show that G is Eulerian.
06:15
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.
09:16
4] Draw the Graph that has a Hamiltonian path put does not have a Hamiltonian circuit.
04:51
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.
06:44
Module-3
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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
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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
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1] State and prove Euler’s formula that gives the number of regions in any planar graph
10:45
2] Define planar and non-planar graphs. State Kuratowski’s theorem. Draw Kuratowski’s two graphs.
06:08
3] If G is a simple planar Graph with atleast three vertices then show that
08:53
4] Prove that planar Graph contains a vertex of degree atmost 5
05:43
5] Draw the Geometric Dual of the given graph
16:32
Module-5
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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
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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.
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6] Define Covering and minimal covering of a graph. Obtain two minimal coverings from the given graph.
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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 .
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8] State and prove Five color theorem.
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Graph Theory || BCS405B || Model Question Paper + Important Questions with Solutions (EXPLAINED) || CSE stream || 2022 Scheme || Video Course and Study Material
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