12 citations · 71 across the 46 of their papers we have counts for
8 papers · 1 filter
Characterizing graphs of maximum principal ratio
Michael Tait, Josh Tobin
The principal ratio of a connected graph, denoted , is the ratio of the maximum and minimum entries of its first eigenvector. Cioabă and Gregory conjectured that the graph on…
On a problem of Neumann
Michael Tait
A conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of e…
Spectral bounds for the -independence number of a graph
Aida Abiad, Sebastian Cioabă, Michael Tait
In this paper, we obtain two spectral upper bounds for the -independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than $k…
On the distance spectra of graphs
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +8
The distance matrix of a graph is the matrix containing the pairwise distances between vertices. The distance eigenvalues of are the eigenvalues of its distance matrix and…
Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +4
We establish a conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-conca…
A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results
Thang Pham, Michael Tait, Craig Timmons +1
We prove a Szemerédi-Trotter type theorem and a sum-product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and o…