Mathematics · Discrete Mathematics
Gallai Independence–Vertex-Cover Identity Calculator
Calculate total vertex count from maximum independent-set size and minimum vertex-cover size.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a+b with maximum independent-set size=72 and minimum vertex-cover size=48.
- total vertex count=120.
Understand Gallai Independence–Vertex-Cover Identity
One idea, three depths
Choose how deeply to explain Gallai Independence–Vertex-Cover Identity
Gallai Independence–Vertex-Cover Identity: Calculate total vertex count from maximum independent-set size and minimum vertex-cover size.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Gallai Independence–Vertex-Cover Identity to answer this question: calculate total vertex count from maximum independent-set size and minimum vertex-cover size? Enter maximum independent-set size and minimum vertex-cover size; the calculator shows total vertex count. For example: maximum independent-set size=72 and minimum vertex-cover size=48 produce total vertex count=120. The answer tells you total vertex count.
Age 15Explain it to a 15-year-oldConnect it to the formula
In any finite graph, maximum independent-set size plus minimum vertex-cover size equals the number of vertices. This page evaluates the relationship directly. The rule is c=a+b. Its input values are maximum independent-set size, minimum vertex-cover size, and the main result is total vertex count. For example: maximum independent-set size=72 and minimum vertex-cover size=48 produce total vertex count=120.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated gallai independence–vertex-cover identity relation over the valid real-number domain stated below. The implemented relation is c=a+b, evaluated from maximum independent-set size, minimum vertex-cover size to produce total vertex count. In any finite graph, maximum independent-set size plus minimum vertex-cover size equals the number of vertices. This page evaluates the relationship directly. The independent set and vertex cover must be optimal and refer to the same graph.
Inputs and valid domain
- maximum independent-set size must be a finite real number.
- minimum vertex-cover size must be a finite real number.
Important boundary: The independent set and vertex cover must be optimal and refer to the same graph.
The formula
c=a+b
How the calculator works through it
It substitutes maximum independent-set size, minimum vertex-cover size into the formula and exposes every numerical step above. The main output is total vertex count.
Read the result correctly
The total vertex count is the direct answer to “calculate total vertex count from maximum independent-set size and minimum vertex-cover size.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
maximum independent-set size=72 and minimum vertex-cover size=48 produce total vertex count=120.
Where this model stops being reliable
The independent set and vertex cover must be optimal and refer to the same graph.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Gallai Independence–Vertex-Cover Identity works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Gallai Independence–Vertex-Cover Identity uses c=a+b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Sets, membership and finite collections
Sets provide the objects and membership rules that give Gallai Independence–Vertex-Cover Identity its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Gallai Independence–Vertex-Cover Identity to systematic counting and arrangement problems.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read maximum independent-set size, minimum vertex-cover size.
- Evaluate the principal relationship: c=a+b.
- Return total vertex count and check the domain conditions described above.
Python
from math import *
def gallai_independence_cover_identity_calculator(a, b) -> float:
return (a + b)
assert abs(gallai_independence_cover_identity_calculator(72, 48) - 120) < 1e-6 * max(1.0, abs(120))
C
#include <assert.h>
#include <math.h>
double gallai_independence_cover_identity_calculator(double a, double b) {
return (a + b);
}
int main(void) {
const double expected = 120;
const double actual = gallai_independence_cover_identity_calculator(72, 48);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double gallai_independence_cover_identity_calculator(double a, double b) {
return (a + b);
}
int main() {
constexpr double expected = 120;
const double actual = gallai_independence_cover_identity_calculator(72, 48);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double gallai_independence_cover_identity_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global gallai_independence_cover_identity_calculator
section .text
gallai_independence_cover_identity_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = gallai_independence_cover_identity_calculator(a, b)
result = (a + b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a + b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Gallai Independence–Vertex-Cover Identity Calculator. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator
MLA 9
MW SysArc. “Gallai Independence–Vertex-Cover Identity Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Gallai Independence–Vertex-Cover Identity Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator.
Harvard
MW SysArc (2026) ‘Gallai Independence–Vertex-Cover Identity Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_gallai_independence_cover_identity_calculator_2026,
author = {{MW SysArc}},
title = {Gallai Independence–Vertex-Cover Identity Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Gallai Independence–Vertex-Cover Identity Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/gallai-independence-cover-identity-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Gallai Independence–Vertex-Cover Identity do?
Calculate total vertex count from maximum independent-set size and minimum vertex-cover size.
How does the Gallai Independence–Vertex-Cover Identity work?
The calculator applies c=a+b. In any finite graph, maximum independent-set size plus minimum vertex-cover size equals the number of vertices. This page evaluates the relationship directly.
What can I learn from the Gallai Independence–Vertex-Cover Identity?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .