27th Conference of the International Linear Algebra Society (ILAS 2026)

Moore-Penrose inverse of the Laplacian matrix of an unicyclic graph

May 20, 2026, 11:50 AM

25m

McBryde Hall 113

Minisymposium Talk Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Speaker

Ranveer Singh (IIT Indore, India)

Description

The Moore-Penrose inverse of a Laplacian matrix is a fundamental object in algebraic graph theory and network analysis, but explicit formulas are known only for restricted graph families. In this paper, we study the Laplacian matrix of unicyclic graphs, and derive an explicit closed-form formula for the Moore-Penrose inverse which can be calculated in $O(n^2)$, where n is the size of the graph.