Chromatic Polynomial Calculator
Calculate P(G,k) - the number of proper k-colorings of a graph.
Graph Parameters
Chromatic Polynomial
P(K_4, k) = k(k-1)(k-2)(k-3)
Falling factorial: each vertex needs a different color from all previous.
P(G,k) Values
k=1
0
k=2
0
k=3
0
k=4
24
k=5
120
k=6
360
k=7
840
Number of 5-colorings
P(G,5) = 120
Chromatic Number
chi = 4
Vertices
4
Properties
Smallest k with P(G,k) > 04
Polynomial degree4
About Chromatic Polynomial
- P(G,k) counts proper k-colorings of graph G
- Chromatic number is smallest k where P(G,k) > 0
- The polynomial has degree n (number of vertices)
- Leading coefficient is always 1
- Deletion-contraction: P(G,k) = P(G-e,k) - P(G/e,k)
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.