Linear graph

The linear graph ${\displaystyle P_{6}}$

A linear graph or path graph is a graph that consists of only one path . Linear graphs are simple examples of trees . They have no branches, so the middle nodes are degree 2 and the end nodes are degree 1. The linear graph with nodes is denoted by. ${\displaystyle n}$ ${\displaystyle P_{n}}$

Graceful lettering

Linear graphs are graceful graphs . A graceful lettering is created when the nodes are labeled with the numbers . This lettering is bipartite. ${\displaystyle 1,n,2,n-1,3,n-3,\ldots }$

The following drawing shows a corresponding graceful label for the linear graph with five nodes.

See also

• Circle graph
• Star graph
• Ladder graph

Individual evidence

1. ↑ Michelle Edwards, Lea Howard: A survey of graceful trees . In: Atlantic Electronic Journal of Mathematics . 1, No. 1, 2006, pp. 5-29.