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a. Write down the degree of the 16 vertices in the graph below: 14 11 13 12 15 7 10 16

a. Write down the degree of the 16 vertices in the graph below: 14 11 13 12 15 7 10 16

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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 mumber 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. a. Write down the degree of the 16 vertices in the graph below: 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
Transcribed Image Text: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 mumber 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. a. Write down the degree of the 16 vertices in the graph below: 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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