Search results for graph-theory

111 votes
9 answers
1
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
38 votes
9 answers
5
32 votes
14 answers
6
Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...
32 votes
9 answers
7
33 votes
5 answers
9
The minimum number of edges in a connected cyclic graph on $n$ vertices is:$n-1$$n$$n+1$None of the above
76 votes
5 answers
10
Which of the following graphs has an Eulerian circuit?Any $k$-regular graph where $k$ is an even number.A complete graph on $90$ vertices.The complement of a cycle on $25...
28 votes
6 answers
13
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is...
73 votes
6 answers
15
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ?$1$$2$$3$$n$
65 votes
9 answers
16
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...