Given is a weighted complete graph where every weigth is a positive ineger. Let n be the amount of vertices.
I have to prove that the number of edges of a minimum spanning tree of that graph is equal to n-1.
2026-03-31 10:01:01.1774951261
Minimum spanning tree edge count
3.5k 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 PROOF-WRITING
- how is my proof on equinumerous sets
- Do these special substring sets form a matroid?
- How do I prove this question involving primes?
- Total number of nodes in a full k-ary tree. Explanation
- Prove all limit points of $[a,b]$ are in $[a,b]$
- $\inf A = -\sup (-A)$
- Prove that $\sup(cA)=c\sup(A)$.
- Supremum of Sumset (Proof Writing)
- Fibonacci Numbers Proof by Induction (Looking for Feedback)
- Is my method correct for to prove $a^{\log_b c} = c^{\log_b a}$?
Related Questions in TREES
- Explanation for the static degree sort algorithm of Deo et al.
- Finding height of a $k$-ary tree
- Clique-width of a tree
- count "informative" paths in tree
- If the weight of edge E $e$ of an MST is decreased by $\delta$. Could total weight of MST decrease by more than $\delta$.
- Probability of two randomly selected leaves of a tree to be connected only at the root
- Proof in graph theory: maximum degree and number of leaves.
- Graph Theory: Number of vertices in a tree.
- The number of, and an enumeration for, the set of full subtrees of the full complete binary tree
- Is the maximum link length function convex?
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?
A spanning tree of a connected graph $G$ by definition is a tree whose vertex set is all of $V(G)$. All trees $T$ satisfy the equation $E(T) = V(T) -1$. Let $V(G) =n$.
Therefore, if $T$ is spanning tree of $G$, $T$ has $E(T) = V(T) -1 = V(G) -1 = n-1$.