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A k-regular bipartite graph is the one in which degree of each vertices is k for all the vertices in the graph. Given that the bipartitions of this graph are U and V respectively. What is the relation between them?

Correct Answer: Number of vertices in U=Number of vertices in V
We know that in a bipartite graph sum of degrees of vertices in U=sum of degrees of vertices in V. Given that the graph is a k-regular bipartite graph, we have k*(number of vertices in U)=k*(number of vertices in V).

There are four students in a class namely A, B, C and D. A tells that a triangle is a bipartite graph. B tells pentagon is a bipartite graph. C tells square is a bipartite graph. D tells heptagon is a bipartite graph. Who among the following is correct?

Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?

Given G is a bipartite graph and the bipartitions of this graphs are U and V respectively. What is the relation between them?

An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?

A complete bipartite graph is a one in which each vertex in set X has an edge with set Y. Let n be the total number of vertices. For maximum number of edges, the total number of vertices hat should be present on set X is?

The rear window of an automobile is made of thick glass i.e. AB = 5 mm and thermal conductivity is 0.8 W/m degree. To defrost this window, a thin transparent film type heating element has been fixed to its inner surface. For the conditions given below, determine the electric power that must be provided per unit area of window if a temperature 5 degree Celsius is maintained at its outer surface. Interior air temperature and the corresponding surface coefficient are 20 degree Celsius and 12 W/m2 degree. Surrounding air temperature and the corresponding surface coefficient are – 15 degree Celsius and 70 W/m2 degree. Electric heater provides uniform heat flux

How many of the following statements are correct? i) All cyclic graphs are complete graphs. ii) All complete graphs are cyclic graphs. iii) All paths are bipartite. iv) All cyclic graphs are bipartite. v) There are cyclic graphs which are complete.

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?

G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is ______