Andrea Paone

Line-graph inertia of roses and generalized theta graphs

For a graph G, the adjacency inertia of the line graph L(G) is determined by the number of eigenvalues of the signless Laplacian Q(G) above, equal to, and below 2. We compute the inertia of Q(G) - 2I, and hence the inertia of the adjacency matrix of L(G), exactly, including every...

Unbounded Signature of Line Graphs: Counterexamples and Transfer Principles

Akbari, Elphick, Kumar, Pragada, and Tang conjectured that every connected graph satisfies a one-unit upper bound between the positive and negative adjacency inertia indices of its line graph. Version 1 exhibited a connected simple counterexample with line-graph inertia (9, 0, 7)...