List of top Mathematics Questions on Graph Theory

Which one of the following options is always true?

In a simple graph, which of the following statements is/are true?
(I) Adjacency matrix is symmetric.
(II) Trace of the adjacency matrix is 1.

The coefficient of \( x^{50} \) in \( (1 + x)^{101} (1 - x + x^2)^{100} \) is:

The number of phone calls (in thousands) are made by a telephone company for five weeks as given below:

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
No. of Telephone calls	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Taking a period of moving averages as 3 weeks, the graph of moving averages can be depicted directly as :

In a simple regular graph, total degree is 28. If the graph has more than one cycle in it, then the degree of each vertex is

The vertex connectivity of any tree is

The adjoining graph

For what values of n is the graph $K_n$ Eulerian?

In a tree on a vertices there is exactly one vertex with degree 2 and remaining vertices are of degree either 1 or 3. Then the number of pendant vertices is

Is it possible for wheel $W_n$ ($n \ge 3$) to be bipartite?