This is from my homework.
Let $Q_n$ be the graph with vertex set $\{1, 2, \ldots, n\}$. Two vertices are adjacent if and only if their greatest common divisor is $1$. Give the clique number of $Q_{10}$ and draw a maximum clique of it.
2026-03-28 10:35:27.1774694127
Clique number and maximum clique of gcd-based graph
133 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GRAPH-THEORY
- characterisation of $2$-connected graphs with no even cycles
- Explanation for the static degree sort algorithm of Deo et al.
- A certain partition of 28
- decomposing a graph in connected components
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Fake induction, can't find flaw, every graph with zero edges is connected
- Triangle-free graph where every pair of nonadjacent vertices has exactly two common neighbors
- Inequality on degrees implies perfect matching
- Proving that no two teams in a tournament win same number of games
- Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one
Related Questions in DIVISIBILITY
- Reciprocal-totient function, in term of the totient function?
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Positive Integer values of a fraction
- Reciprocal divisibility of equally valued polynomials over a field
- Which sets of base 10 digits have the property that, for every $n$, there is a $n$-digit number made up of these digits that is divisible by $5^n$?
- For which natural numbers are $\phi(n)=2$?
- Interesting property about finite products of $111..1$'s
- Turn polynomial into another form by using synthetic division
- Fractions of the form $\frac{a}{k}\cdot\frac{b}{k}\cdot\frac{c}{k}\cdots=\frac{n}{k}$
- Proof: If $7\mid 4a$, then $7\mid a$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
The clique number is $5$. Note that there can be at most one even number in a clique, as two even numbers would have a common factor of $2$. Also note that $3$ and $9$ cannot be in the same clique as $3$ divides both. So not all odd numbers can be used. This gives us a maximum bound of $5$ numbers in a clique. $\{1, 2, 3, 5, 7 \}$ suffices to show that this is possible.