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Recent questions tagged goclasses2024-dm-5-weekly-quiz

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 2
Let $\text{G}$ be the following set of undirected connected graphs $:$ $\text{G} = \{ g \mid g \;\text{is a complete graph on}\; n\; \text{vertices where}\; 1\leq n \leq 10 \;\text{OR} \;g$ is a cycle graph on ... $a$ is isomorphic to $b.$ How many equivalence classes will be there for $\text{R}?$

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 4
The number of simple undirected graphs with $6$ labeled vertices and exactly $3$ edges is _________

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 6
Let $\text{G = (V, E)}$ be a finite directed acyclic graph with $|\text{E}| > 0.$ Which of the following is not necessarily true? $\text{G}$ has a vertex with no incoming edge. $\text{G}$ has a ... no outgoing edge. $\text{G}$ has an isolated vertex, that is, one with neither an incoming edge nor an outgoing edge. None

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 7
A Hamiltonian circuit in a graph is a closed path that visits every vertex in the graph exactly once. A Hamiltonian circuit ends up at the vertex from where it started. If a graph has some Hamiltonian circuit, then the graph is called a ... following is/are a hamiltonian graph? $\text{G1}$ $\text{G2}$ $\text{G3}$ $\text{G4}$

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 8
Let $\text{G}$ be a simple graph where $\text{V(G)} = \{1, 2, \dots , 100\}$ and there is an edge between two distinct vertices $a$ and $b$ iff $a$ divides $b.$ Which of the following statements are true for $\text{G}?$ ... $\text{G}$ is $1.$ $\text{G}$ is connected. The diameter of $\text{G}$ is $6.$

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 11
Let $\text{K}(4,6)$ be the complete bipartite graph on $10$ vertices, having $4$ vertices in one part and having $6$ ... is a complete graph. Either $\text{K}(m,n)$ OR complement of $\text{K}(m,n)$ is dis-connected.

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 13
For the following graph, what is the summation of chromatic number and matching number?

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 18
Which of the following statements about simple graphs are true ? Two complete graphs on $m,n$ vertices respectively, are isomorphic to each other if and only if $m=n.$ Wheel graph on $n$ vertices, $n \geq 4,$ is never ... always planar graph. Complement of a cycle graph on $n$ vertices is connected if and only if $n \geq 5.$

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 22
Which of the following statements are correct? The complement of a simple disconnected graph must be connected. The complement of a simple connected graph must be disconnected. The complement of complete bipartite graph $\text{K}(4,6)$ ... . Then $\text{G}$ must have $4k$ or $4k + 1$ vertices for some integer $k.$

GO Classes asked in Graph Theory May 11, 2022

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GO Classes Test Series 2024 | Discrete Mathematics | Test 5 | Question: 23
The height of a rooted tree is the maximum height of any leaf. The length of the unique path from a leaf of the tree to the root is, by definition, the height of that leaf. A rooted tree in which each non-leaf vertex has at ... maximum height $h = L-1.$ It is possible to have a binary tree with $35$ leaves and height $100.$

GO Classes asked in Graph Theory May 11, 2022

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