On the Fixed Degree Tree Graph

Abstract

A 2-switch on a simple graph G consists of deleting two edges {u, v} and {x, y} of G and adding the edges {u, x} and {v, y}, provided the resulting graph is a simple graph. It is well known that if two graphs G and H have the same set of vertices and the same degree sequence, then H can be obtained from G by a finite sequence of 2-switches. While the 2-switch transformation preserves the degree sequence other conditions like connectivity may be lost. We study the restricted case where 2-switches are applied to trees to obtain trees.