Zeru Zhu

Maximizing Algebraic Connectivity with $2(n-2)$ Edges: The Large Vertex Number Case

Kolokolnikov conjectured that, among finite simple graphs on $n$ vertices with exactly $2(n-2)$ edges, the complete bipartite graph $K_{2,n-2}$ maximizes algebraic connectivity. We prove the conjectured statement for every $n\ge123$: every such graph has algebraic connectivity at most $2$, while $K_{2,n-2}$ attains $2$...