On Minimum Algebraic Connectivity of Tricyclic Graphs

Abstract

‎Consider a simple‎, ‎undirected graph $ G=(V,E)$‎, ‎where $A$ represents the adjacency matrix and $Q$ represents the Laplacian matrix of $G$‎. ‎The second smallest eigenvalue of Laplacian matrix of $G$ is called the algebraic connectivity of $G$‎. ‎In this article‎, ‎we present a Python program for studying the Laplacian eigenvalues of a graph‎. ‎Then‎, ‎we determine the unique graph of minimum algebraic connectivity in the set of all tricyclic graphs‎.

Keywords

• algebraic connectivity‎
• ‎bicyclic graph‎
• ‎tricyclic graph‎
• ‎python programming language‎