ABSTRACT
This article describes the structure of the graph minimizing the algebraic connectivity among all connected graphs made with some given blocks with fixed number of pendant blocks, the blocks that have exactly one point of articulation. As an application, we conclude that over all graphs made with given blocks, the algebraic connectivity is minimum for a graph whose block structure is a path.
Acknowledgements
The authors sincerely thank the referees and editors for carefully reading the manuscript and their suggestions. The financial assistance for Kuldeep Sarma was provided by CSIR, India, through a JRF.
Notes
No potential conflict of interest was reported by the authors.