(3.5) Graphs 1) List the degrees of the verticies of each of these graphs. Verif

Question

(3.5) Graphs

1) List the degrees of the verticies of each of these graphs. Verify both parts of Thm. in each case

I couldn't get the picture but it's in the book

2) if possible, give an example of a graph with order 6 such that

a) the verticies have degrees 1, 1, 1, 1, 1, 5

b) the verticies have degrees 1, 1, 1, 1, 1, 1

d) the verticies have degrees 1, 2, 2, 2, 3,

3 If possible, give an example of a graph

a) with order 6 and size 6

c) with order 3 and size 4

d) with order 6 and size 3

4) For the graph at the right (picture in the book), find all the subgraphs

a) two verticies

b) with three vertices

7) Give an example of a graph with 6 verticies having

degrees 1, 1, 2, 2, 2, 2 that is

a) connected

b) disconnected

8. Give an example of a graph with 6 verticies having

a) one component

b) two components

c) three components

d) six components

11 Verify these properties for the distance between verticies in a connected graph

a) d(u, v) (more than or equal to ) 0

b) d( u, v) = 0 iff u = v

Explanation / Answer

2. b a simple hexagon with just the boundaries..

2. a hexagon with exactly one vertex connected to all others !!

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