Solving line Graphs

Introduction

         In graph theory, the line graph L(G) of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this. Other terms used for the line graph include edge graph, the theta-obrazom, the covering graph, the derivative, the edge-to-vertex dual, the interchange graph, the adjoint, the conjugate, the derived graph, and the representative graph.

 

Number line for solving line graphs:

 

Line Graph:

  •  A line graph is a graphical representation of a group of data by line.

  • The group of data is graphed on a graph with even spaces. Then the line is marked to connect the data points.

  • The line graph is used for comparing the various data, which is larger and smaller.

Graphing numbers:

     The graphing numbers is a graphical representation of integers with inequalities in horizontal line and it is a visualizing result of number line with simple steps.

 

Steps & Examples for solving line graphs:

 

Steps for solving line graphs:

The following steps are needed for solving line graph.

Step 1: Draw a horizontal straight line (x-axis) and mostly the number line is represented as horizontal line

Step 2: Draw a vertical straight line (y-axis). (if needed).

Step 3: Draw the arrow on both ends of graph line.

Step 4: Point the origin zero on the graph line.

Step 5: To write the positive integer on the right side of the origin with even spaces (for x-axis).

Step 6: To write the positive integer on the top side of the origin (for y-axis).

Step 7: To write the negative integer on the left side of the origin with even spaces (for x-axis).

Step 8: To write the negative integer on the bottom side of the origin (for y-axis).

Step 9: Mark all integers over the number line.

Step 10: Plot the answers for given question.

 

Examples for solving line graphs are as follows:

Example1:

Graph

2) Solving the following inequality for line graph:25b < 200

(i) ‘b’ is a natural number,

(ii) ‘b’ is an integer.

Solution:

      Given 25 b < 200

          25b/ 25< 200 / 25          

                     b< 8.

(i) When ‘b’ is a natural number, then graph of ‘b’,

                            1, 2, 3, 4, 5, 6, 7.

     The solution set is {1, 2, 3, 4, 5, 6 and 7}.

(ii) When ‘b’ is an integer, then the solution is given as,

                     ..., – 3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7.

     The solution set is {...,–3, –2,–1, 0, 1, 2, 3, 4, 5, 6 and 7}

Therefore, graph of ‘b’ on number line