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Recent questions tagged graph-connectivity

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2 answers
61
CMI2019-B-4
Consider the assertion: Any connected undirected graph $G$ with at least two vertices contains a vertex $v$ such that deleting $v$ from $G$ results in a connected graph. Either give a proof of the assertion, or give a counterexample (thereby disproving the assertion).
Consider the assertion: Any connected undirected graph $G$ with at least two vertices contains a vertex $v$ such that deleting $v$ from $G$ results in a connected graph....
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1 votes
2 answers
63
CMI2018-B-3
Let $G$ be a simple graph on $n$ vertices. Prove that if $G$ has more than $\binom{n-1}{2}$ edges then $G$ is connected. For every $n>2$, find a graph $G_{n}$ which has exactly $n$ vertices and $\binom{n-1}{2}$ edges, and is not connected.
Let $G$ be a simple graph on $n$ vertices.Prove that if $G$ has more than $\binom{n-1}{2}$ edges then $G$ is connected.For every $n>2$, find a graph $G_{n}$ which has exa...
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1 votes
1 answer
66
ISI2017-PCB-CS-1(b)
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.
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33 votes
14 answers
67
GATE CSE 2019 | Question: 12
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 $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
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}...
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1 answer
69
doubt
what is the diameter and radius of the complete bipartite graph?
what is the diameter and radius of the complete bipartite graph?
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