On Operations in which Graphs are Appended to Trees

Document Type

Peer-Reviewed Article

Publication Date

2004

Abstract

We consider the effects on the algebraic connectivity of various graphs when vertices and graphs are appended to the original graph. We begin by considering weighted trees and appending a single isolated vertex to it by adding an edge from the isolated vertex to some vertex in the tree. We then determine the possible set vertices in the tree that can yield the maximum change in algebraic connectivity under such an operation. We then discuss the changes in algebraic connectivity of a star when various graphs such as trees and complete graphs are appended to its pendant vertices.

Comments

AMS Subject Classifications: 05C50; 15A18; 15A48

DOI

10.1080/03081080310001617759

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