Chapter 5

Question 1

What is traversibility and how to figure

Answer 1

Ability to draw without taking the pen off the paper and without going over the same edge twice.
To determine reversibility
all vertices have even edges connecting to them and
if there are two vertices with two odd edges connecting to them

Question 2

What is a loop?

Answer 2

Any graph or network with an edge that starts and ends at the same vertex said to have contained a loop

Question 3

What is multiple edges?

Answer 3

If two or more edges connect the same to the same two vertices

Question 4

What is a weighted graph or a weighted network?

Answer 4

Each edge is worth a particular weight be at a distance cost time and etc

Question 5

What is an adjacent vertices?

Answer 5

If two vertices are connected by the same edge

Question 6

What is a directed graph or digraphs?

Answer 6

Graph set up directed edges or arcs

Question 7

What is undirected graphs?

Answer 7

Graphs with no directed edges

Question 8

What is a simple graph?

Answer 8

A simple graph is an undirected unweighted graph with no loop and no multiple edges

Question 9

What is a walk?

Answer 9

Each vertex and sequence is joined to the next vertex in sequence by an edge

Question 10

What is a closed walk or cycle?

Answer 10

That starts and finishes at the same vertex

Question 12

What is an open walk?

Answer 12

Any walk that does not end at starting vertex

Question 13

What is a path?

Answer 13

A walk that does not include to repeat it uses of edges and vertices

Question 14

What is a length?

Answer 14

The number of edges used

Question 15

What is a trail?

Answer 15

Walk with no repeated edges

Question 16

What is it connected graph or connected network?

Answer 16

An undirected graph or network where every vertex is connected to every other vertex

Question 17

What is a complete graph?

Answer 17

Simple graph in which every vertex is connected to every other vertex by a single edge in each case

Question 18

What is KN?

Answer 18

Complete graph with n number of vertices

Question 19

What is a bridge?

Answer 19

A bridge is a connected graph where the removal of an edge leaves the graph to be disconnected

Question 20

What is a planar graph?

Answer 20

A graph that can be drawn in plane without its edge crossing over

Question 21

What is Euler’s rule?

Answer 21

V +F =e+2

Question 22

What is a bipartite graph?

Answer 22

A bot graph has two sides and vertices have been separated in 2 set.
No two vertices on the left or the right is adjacent to each other

Question 23

What is degree or order of vertex?

Answer 23

Number of edges meeting at the vertex

Question 24

What is an in degree vertex?

Answer 24

Number of edges coming in the vertex

Question 25

What is out of degree vertex?

Answer 25

Number of edges going out the vertex

Question 26

What is Eulerian Trail?

Answer 26

connected graph that travels every edge once and the repeated vertices is permitted

Question 27

What is a tree?

Answer 27

A tree is a simple connected graph that contains no cycle loops or multiple edges

Question 28

What is Eulerian circuit or eulerian graph

Answer 28

Trail is close-finishes and starts at the same vertex Traversable Zero odd vertices Travels every edge once

Question 29

What is a semi Eulerian graph?

Answer 29

Trail is open -does not start and finish at the same vertex Traversable Exactly two odd vertices Travels every edge

Question 30

What is Hamiltonian path?

Answer 30

A path in the graph that visits every vertex in the graph only once with the possible exception of visiting the first vertex again at the end. Do not have to include every edge

Question 31

What is Hamiltonian cycle or Hamiltonian

Answer 31

If the path is closed, it is said to be a Hamiltonian cycle or Hamiltanion . Includes all verticies

Question 32

What is a semi Hamiltonian graph?

Answer 32

If the path is closed, it is said to be a Hamiltonian cycle or Hamiltanion . Includes all vertices