3 citations · 4 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
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…
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.