3 citations · 4 across the 12 of their papers we have counts for
13 papers
Resolution of a problem of Mohar on non-positive inertia
Clive Elphick, Hitesh Kumar, Shivaramakrishna Pragada +1
For a graph of order , its positive, negative and non-positive inertia is the number of positive, negative and non-positive eigenvalues of its adjacency matrix , respe…
Eigenvalues of Universal Covers and the Matching Polynomial
Thomás Jung Spier
In this work, we prove that the universal and maximal abelian covers of a finite multi-graph have the same eigenvalues. This result strengthens a recent theorem of Li, Magee, Sabri…
Orthogonal polynomials, quantum walks and the Prouhet-Tarry-Escott problem
Frederico Cançado, Gabriel Coutinho, Thomás Jung Spier
This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs…
Efficient reconstruction of the characteristic polynomial
Thomás Jung Spier
The polynomial reconstruction problem, introduced by Cvetković in 1973, asks whether the characteristic polynomial of a graph with at least vertices can be reconstruc…
Conic programming to understand sums of squares of eigenvalues of graphs
Gabriel Coutinho, Thomás Jung Spier, Shengtong Zhang
In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency mat…
Sums of squares of eigenvalues and the vector chromatic number
Gabriel Coutinho, Thomás Jung Spier
In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided…
No perfect state transfer in trees with more than 3 vertices
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are and . This answers a question first asked by Godsil in 2012 an…
The spectrum of symmetric decorated paths
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
The main result of this paper states that in a rooted product of a path with rooted graphs which are disposed in a somewhat mirror-symmetric fashion, there are distinct eigenvalues…
Irrational quantum walks
Gabriel Coutinho, Pedro Ferreira Baptista, Chris Godsil +2
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenva…
Strong cospectrality in trees
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
We prove that no tree contains a set of three vertices which are pairwise strongly cospectral. This answers a question raised by Godsil and Smith in 2017.
A refined Gallai-Edmonds structure theorem for weighted matching polynomials
Thomás Jung Spier
In this work, we prove a refinement of the Gallai-Edmonds structure theorem for weighted matching polynomials by Ku and Wong. Our proof uses a connection between matching polynomia…
On Means of Near Continued Fractions
Thomás Jung Spier
In this work, we present continued fractions for the arithmetic, geometric, harmonic and cotangent means of and , and some of the…
On Graph Continued Fractions and the Heilmann-Lieb Theorem
Thomás Jung Spier
Inspired by Viennot's observation that matching polynomials are numerators of branched continued fractions we present a proof of the Heilmann-Lieb Theorem.