University of Kashan Mathematics Interdisciplinary Research 2538-3639 9 2 2024 06 01 On Minimum Algebraic Connectivity of Tricyclic Graphs 185 197 114327 10.22052/mir.2024.253568.1437 EN Hassan Taheri ‎Faculty of Mathematical Science, ‎Department of Pure Mathematics,‎ ‎University of Kashan,‎ ‎Kashan 87317-51167‎, ‎I. R. Iran Gholam Hossein Fath-Tabar ‎Faculty of Mathematical Science, ‎Department of Pure Mathematics,‎ ‎University of Kashan,‎ ‎Kashan 87317-51167‎, ‎I. R. Iran Journal Article 2023 09 25 ‎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. https://mir.kashanu.ac.ir/article_114327_65963fe40f3d819f233406d3954b9d84.pdf