An Upper Bound on the Algebraic Connectivity of Outerplanar Graphs

Authors

Jason J. Molitierno, Sacred Heart UniversityFollow

Document Type

Peer-Reviewed Article

Publication Date

8-2017

Abstract

In this paper, we determine upper bounds on the algebraic connectivity, denoted as a(G), of maximal outerplanar graphs. We show that if G is a maximal outerplanar graph on n≥12 vertices not of the form K₁∨P_n−1, then a(G)≤1 with equality holding for exactly two maximal outerplanar graphs on 12 vertices. We show this by assigning labels y₁,…,y_n to the vertices and showing the existence of vertex labellings such that.

Comments

© 2017 Elsevier B.V. All rights reserved.

DOI

10.1016/j.disc.2017.03.015

Recommended Citation

Molitierno, J.J. (2017). An upper bound on the algebraic connectivity of outerplanar graphs. Discrete Mathematics, 340(8), 1851-1870. doi:10.1016/j.disc.2017.03.015