Minimal edge extensions of palm trees

Minimal edge extension of graphs can be regarded as a model of optimal edge fault tolerant implementation of a system. The problem of finding the minimal edge extensions of an arbitrary graph is NP-complete, that's why it is of interest to find classes of graphs for which it is possible to build a minimal edge extension analytically. This paper is about of the one-edge extensions of a graphs from a special class named palm trees. In this paper presents a kind of one-edge extension for some palm trees and the proof that it is minimal.