Path graph

A linear graph or path graph is a graph, which consists only of a path. Linear graphs are simple examples of trees. You have no branches, so that the average node degree 2, and the terminal nodes have degree 1. The linear graph with nodes is denoted by.

Graceful labeling

Linear graphs are graceful graph. A graceful labeling arises when the nodes are labeled with the numbers. This label is bipartite.

A graceful labeling for the corresponding linear graph with five nodes shown in the following drawing.