In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labelstraditionally called "colors" to elements of a graph subject to certain constraints. In its simplestform, it is a way of coloring the vertices of a graph such that no two adjacent vertices share thesame color; this is called a vertex coloring. The chromatic number of a graph is the leastnumber of colors required to do a coloring of a graph.ExampleHere in this graph the chromatic number is 3 since we used 3 colorsThe degree of a vertex v in a graph (without loops) is the number of edges at v. Ifthere are loops at v each loop contributes 2 to the valence of v.A graph is connected if for any pair of vertices u and v one can get from u to v bymoving along the edges of the graph. Such routes that move along edges are knownby different names: edge progressions, paths, simple paths, walks, trails, circuits,cycles, etc.14131215710161. Is there a connected graph whose degree are:a. 5, 3, 2, 2, 2, 1, 1b. 8, 6c. 5, 5, 3, 3, 3, 2, 2, 2, 2, 2d. 5, 3, 3, 3, 2, 2, 2, 2, 2e. 4, 4, 4, 4, 4, 4, 4, 4, 4

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1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

Advanced Engineering Mathematics

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ISBN:9780470458365

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Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Question

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels
traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest
form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the
same color; this is called a vertex coloring. The chromatic number of a graph is the least
number of colors required to do a coloring of a graph.
Example
Here in this graph the chromatic number is 3 since we used 3 colors
The degree of a vertex v in a graph (without loops) is the number of edges at v. If
there are loops at v each loop contributes 2 to the valence of v.
A graph is connected if for any pair of vertices u and v one can get from u to v by
moving along the edges of the graph. Such routes that move along edges are known
by different names: edge progressions, paths, simple paths, walks, trails, circuits,
cycles, etc.
14
13
12
15
7
10
16
1. Is there a connected graph whose degree are:
a. 5, 3, 2, 2, 2, 1, 1
b. 8, 6
c. 5, 5, 3, 3, 3, 2, 2, 2, 2, 2
d. 5, 3, 3, 3, 2, 2, 2, 2, 2
e. 4, 4, 4, 4, 4, 4, 4, 4, 4

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