David Martin Venti

A counterexample to a conjecture of Jia and Song on remoteness and the second largest distance eigenvalue

David Martin Venti

We disprove a conjecture of Jia and Song (J. Inequal. Appl. 2018:69, Conjecture 3.8), later reproduced as Conjecture 1 in the survey of Aouchiche and Rather (Discrete Appl. Math. 353 (2024) 94–120), concerning the sum of the remoteness ρ and the second …

ir, us (code pays fourni par la source)

A counterexample to a conjecture of Jia and Song on remoteness and the second largest distance eigenvalue

David Martin Venti

We disprove a conjecture of Jia and Song (J. Inequal. Appl. 2018:69, Conjecture 3.8), later reproduced as Conjecture 1 in the survey of Aouchiche and Rather (Discrete Appl. Math. 353 (2024) 94–120), concerning the sum of the remoteness ρ and the second …

ir, us (code pays fourni par la source)

Certificates and Lean 4 formalisation for two distinct eigenvalues at the sparsity threshold

David Martin Venti

Lean 4 / Mathlib sources and exact rational certificates supporting the note "A counterexample and a threshold theorem for graphs with two distinct eigenvalues". For a graph G, q(G) is the minimum number of distinct eigenvalues over the real symmetric matrices with …

ir, us (code pays fourni par la source)

A counterexample and a threshold theorem for graphs with two distinct eigenvalues

David Martin Venti

For a graph G on n vertices, q(G) denotes the minimum number of distinct eigenvalues among the real symmetric matrices whose off-diagonal zero pattern is prescribed by G. Barrett, Fallat, Furst, Nasserasr, Rooney and Tait (arXiv:2411.12917; ELA 42 (2026)) conjectured (their Conjecture …

ir, us (code pays fourni par la source)

A counterexample and a threshold theorem for graphs with two distinct eigenvalues

David Martin Venti

For a graph G on n vertices, q(G) denotes the minimum number of distinct eigenvalues among the real symmetric matrices whose off-diagonal zero pattern is prescribed by G. Barrett, Fallat, Furst, Nasserasr, Rooney and Tait (arXiv:2411.12917; ELA 42 (2026)) conjectured (their Conjecture …

ir, us (code pays fourni par la source)

Certificates and Lean 4 formalisation for two distinct eigenvalues at the sparsity threshold

David Martin Venti

Lean 4 / Mathlib sources and exact rational certificates supporting the note "A counterexample and a threshold theorem for graphs with two distinct eigenvalues". For a graph G, q(G) is the minimum number of distinct eigenvalues over the real symmetric matrices with …

ir, us (code pays fourni par la source)

Explicit bounds for the signless Brouwer conjecture at all k: realisability, a k-free certificate, and the anatomy of the obstruction

David Martin Venti

We study the signless Brouwer conjecture (Ashraf–Omidi–Tayfeh-Rezaie): the inequality S_k(Q) ≤ m + C(k+1,2) for the sum of the k largest eigenvalues of the signless Laplacian Q = D + A of a graph with m edges. Building on the k=3 realisability …

ir, us (code pays fourni par la source)

Structural analysis of the signless Brouwer conjecture: projection thresholds, extremal families, and the Laplacian–signless gap

David Martin Venti

We study the signless Brouwer conjecture (Ashraf–Omidi–Tayfeh-Rezaie): the inequality S_k(Q) ≤ m + C(k+1,2) for the sum of the k largest eigenvalues of the signless Laplacian Q = D + A of a graph with m edges, where C(k+1,2) denotes the binomial …

ir, us (code pays fourni par la source)

Structural analysis of the signless Brouwer conjecture: projection thresholds, extremal families, and the Laplacian–signless gap

David Martin Venti

We study the signless Brouwer conjecture (Ashraf–Omidi–Tayfeh-Rezaie): the inequality S_k(Q) ≤ m + C(k+1,2) for the sum of the k largest eigenvalues of the signless Laplacian Q = D + A of a graph with m edges, where C(k+1,2) denotes the binomial …

ir, us (code pays fourni par la source)

Trophic redundancy, not species diversity, predicts food web structural robustness: edge-level bifurcation analysis across 249 ecosystems

David Martin Venti

The structural mechanisms that confer resilience in food webs remain poorly understood despite decades of research linking biodiversity to ecosystem stability. Here we present an edge-level analytical framework that derives, for each trophic interaction, a closed-form bifurcation threshold from local triangle counts. …

Structural analysis of the signless Brouwer conjecture: projection thresholds, extremal families, and the Laplacian–signless gap

David Martin Venti

Ashraf, Omidi, and Tayfeh-Rezaie conjectured that for every graph G on n vertices with m edges and signless Laplacian eigenvalues q₁ ≥ ⋯ ≥ qₙ ≥ 0, the partial sum Sₖ(Q) = Σᵢ₌₁ᵏ qᵢ satisfies Sₖ(Q) ≤ m + C(k+1, 2) for …

ir, us (code pays fourni par la source)

Eulerian cycle spectrum as molecular descriptor : a structured redundancy analysis on the TDC ADMET benchmark

David Martin Venti

Molecular property prediction for ADMET (absorption, distribution, metabolism, ex-cretion, toxicity) relies on molecular descriptors whose information content varies with the property of interest. We introduce the Eulerian cycle spectrum (ECS), a family of topological graph features derived from the Laplacian and signless …

ir, us (code pays fourni par la source)