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.
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 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:
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