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ACE ACADEMY BOOKLET
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Which of the following is $\textbf{not}$ TRUE?
(a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n.
(b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ $m$ $=$ $n$.
(C) In a cycle graph $C_n$($n \geq$3), Hamiltonian cycle exits for all $n$
(d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.
graphtheory
discretemathematics
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May 26, 2019
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Graph Theory
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`JEET
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Hamiltonian cycle will exist in all of the above mentioned graphs. It won't exist in star graph or complete bipartite graph with minimum number of edges. But as it is mentioned m=n and m,n >=2, hamiltonian cycle will be existing in all graphs. But by going on conditions Option D can be considered as false because it says that wheel graph has hamiltonian cycle if and only if n is even but it will exist in n is odd case also. By going this analogy, I think option:D will be false.
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Jun 4, 2019
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chandan2teja
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ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple nonempty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two nonempty and nonoverlapping subsets $S$ and $T$. Which of the following is true? There are at least two edges that ... $S$ and one end point in $T$ There are exactly one edge that have one end point in $S$ and one end point in $T$
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