Mathematics · Discrete Mathematics
Regular Graph Edge Count vertex count Solver
Rearrange the regular graph edge count relationship and solve for vertex count.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use a=2c/b with undirected edge count=360 and common vertex degree=6.
- vertex count=120.
- Substitution into c=ab/2 reconstructs 360.
Understand Regular Graph Edge Count: solve vertex count
One idea, three depths
Choose how deeply to explain Regular Graph Edge Count: solve vertex count
Regular Graph Edge Count: solve vertex count: Rearrange the regular graph edge count relationship and solve for vertex count.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Regular Graph Edge Count: solve vertex count to answer this question: rearrange the regular graph edge count relationship and solve for vertex count? Enter undirected edge count and common vertex degree; the calculator shows vertex count. For example: vertex count=120 and common vertex degree=6 produce undirected edge count=360. The answer tells you vertex count.
Age 15Explain it to a 15-year-oldConnect it to the formula
The handshaking lemma gives a regular graph one half times vertex count times common degree edges. This page isolates vertex count and verifies it in the original relationship. The rule is a=2c/b. Its input values are undirected edge count, common vertex degree, and the main result is vertex count. For example: vertex count=120 and common vertex degree=6 produce undirected edge count=360.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated regular graph edge count: solve vertex count relation over the valid real-number domain stated below. The implemented relation is a=2c/b, evaluated from undirected edge count, common vertex degree to produce vertex count. The handshaking lemma gives a regular graph one half times vertex count times common degree edges. This page isolates vertex count and verifies it in the original relationship. The product of vertex count and degree must be even for a finite loopless undirected graph.
Inputs and valid domain
- undirected edge count must be a finite real number.
- common vertex degree must be a finite real number.
Important boundary: The product of vertex count and degree must be even for a finite loopless undirected graph.
The formula
a=2c/b
How the calculator works through it
It substitutes undirected edge count, common vertex degree into the formula and exposes every numerical step above. The main output is vertex count, accompanied by Reconstructed undirected edge count.
Read the result correctly
The vertex count is the direct answer to “rearrange the regular graph edge count relationship and solve for vertex count.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
vertex count=120 and common vertex degree=6 produce undirected edge count=360.
Where this model stops being reliable
The product of vertex count and degree must be even for a finite loopless undirected 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 Regular Graph Edge Count: solve vertex count works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Regular Graph Edge Count: solve vertex count uses a=2c/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 Regular Graph Edge Count: solve vertex count its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Regular Graph Edge Count: solve vertex count 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 undirected edge count, common vertex degree.
- Evaluate the principal relationship: a=2c/b.
- Return vertex count and check the domain conditions described above.
Python
from math import *
def regular_graph_edge_count_solve_a(c, b) -> float:
return ((c * 2.0) / b)
assert abs(regular_graph_edge_count_solve_a(360, 6) - 120) < 1e-6 * max(1.0, abs(120))
C
#include <assert.h>
#include <math.h>
double regular_graph_edge_count_solve_a(double c, double b) {
return ((c * 2.0) / b);
}
int main(void) {
const double expected = 120;
const double actual = regular_graph_edge_count_solve_a(360, 6);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double regular_graph_edge_count_solve_a(double c, double b) {
return ((c * 2.0) / b);
}
int main() {
constexpr double expected = 120;
const double actual = regular_graph_edge_count_solve_a(360, 6);
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 regular_graph_edge_count_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global regular_graph_edge_count_solve_a
section .text
regular_graph_edge_count_solve_a:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4000000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = regular_graph_edge_count_solve_a(c, b)
result = ((c * 2.0) / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, b_] := ((c * 2.0) / 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). Regular Graph Edge Count vertex count Solver. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver
MLA 9
MW SysArc. “Regular Graph Edge Count vertex count Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Regular Graph Edge Count vertex count Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver.
Harvard
MW SysArc (2026) ‘Regular Graph Edge Count vertex count Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_regular_graph_edge_count_solve_a_2026,
author = {{MW SysArc}},
title = {Regular Graph Edge Count vertex count Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Regular Graph Edge Count vertex count Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/regular-graph-edge-count-vertex-count-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Regular Graph Edge Count: solve vertex count do?
Rearrange the regular graph edge count relationship and solve for vertex count.
How does the Regular Graph Edge Count: solve vertex count work?
The calculator applies a=2c/b. The handshaking lemma gives a regular graph one half times vertex count times common degree edges. This page isolates vertex count and verifies it in the original relationship.
What can I learn from the Regular Graph Edge Count: solve vertex count?
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 .