What is the chromatic number of PN?

What is the chromatic number of PN?

Hence, the locating chromatic number of the complete graph Kn is n. In addition, for paths and cycles of order n ≥ 3, they proved that χL(Pn) = 3, χL(Cn) = 3 when n is odd, and χL(Cn) = 4 when n is even.

What is the chromatic number for KN?

Explain. Sol: (a) Chromatic number of Kn is n. The colors of all vertices in Kn are distinct because there is an edge between every two vertices. (b) Chromatic number of Ln is n-2.

What is meant by chromatic number?

(definition) Definition: The minimum number of colors needed to color the vertices of a graph such that no two adjacent vertices have the same color.

What is the chromatic number of a tree with n vertices?

Theorem 7.1 Every tree with n ≥ 2 vertices is 2-chromatic. the same colour. Thus T is coloured with two colours. Hence T is 2-chromatic.

What is chromatic number examples?

Example4.3. Thus the chromatic number is 6. The middle graph can be properly colored with just 3 colors (Red, Blue, and Green). For example: There is no way to color it with just two colors, since there are three vertices mutually adjacent (i.e., a triangle).

What is a chromatic number in a graph?

The chromatic number of a graph is the smallest number of colors needed to color the vertices of so that no two adjacent vertices share the same color (Skiena 1990, p. 210), i.e., the smallest value of. possible to obtain a k-coloring.

What is the chromatic number of C5?

5
The star chromatic number of the splitting graph of C5 is 5.

What is chromatic number example?

The chromatic number of a graph is the minimum number of colors needed to produce a proper coloring of a graph. In our scheduling example, the chromatic number of the graph would be the minimum number of time slots needed to schedule the meetings so there are no time conflicts.

Is chromatic number?

The chromatic number, χ(G), of a graph G is the smallest number of colors for V(G) so that adjacent vertices are colored differently. The chromatic number, χ(Sk),of a surface Sk is the largest χ(G) such that G can be imbedded in Sk. We prove that six colors will suffice for every planar graph.

What is the chromatic number of a tree with at least 2 vertices?

So we know that a tree is a graph with unique paths between every pair of vertices. And as a consequence, the chromatic number of a tree with two or more vertices is 2. The proof is just to show you how to color it. You clearly can’t get by with one color if you’ve got any two adjacent vertices.