If G is a colored graph in which each vertex is assigned a color. The chromatic number of a graph G, denoted x(G), is the least number of distinct colors with which G can be properly colored. That is, it is a coloring of the vertices of G with the property that no two adjacent vertices have the same color. In a graph, pairwise non-adjacent vertices or edges are called independent. The maximum number of independent vertices of G if defined as a(G). Prove that in any graph G with n vertices, the number n is less than the multiple of these two values of the Graph.
If G is a colored graph in which each vertex is assigned a color. The chromatic number of a graph G, denoted x(G), is the least number of distinct colors with which G can be properly colored. That is, it is a coloring of the vertices of G with the property that no two adjacent vertices have the same color. In a graph, pairwise non-adjacent vertices or edges are called independent. The maximum number of independent vertices of G if defined as a(G). Prove that in any graph G with n vertices, the number n is less than the multiple of these two values of the Graph.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:3. If G is a colored graph in which each vertex is assigned a color. The
chromatic number of a graph G, denoted x(G), is the least number of
distinct colors with which G can be properly colored. That is, it is a
coloring of the vertices of G with the property that no two adjacent vertices
have the same color. In a graph, pairwise non-adjacent vertices or edges
are called independent. The maximum number of independent vertices
of G if defined as a(G). Prove that in any graph G with n vertices, the
number n is less than the multiple of these two values of the Graph.
(NOTE: Please elaborate on the answer and explain. Please do not copy-paste the answer
from the internet or from Chegg.)
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