17 papers · 1 filter
Strong cocomparability graphs and Slash-free orderings of matrices
Pavol Hell, Jing Huang, Jephian C. -H. Lin
We introduce the class of strong cocomparability graphs, as the class of reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to a…
A zero forcing technique for bounding sums of eigenvalue multiplicities
Franklin H. j. Kenter, Jephian C. -H. Lin
Given a graph , one may ask: "What sets of eigenvalues are possible over all weighted adjacency matrices of ?" (The weight of an edge is positive or negative, while the diago…
On the inverse eigenvalue problem for block graphs
Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc
The inverse eigenvalue problem of a graph aims to find all possible spectra for matrices whose -entry, for , is nonzero precisely when is adjacent to . I…
Complex Hadamard Diagonalisable Graphs
Ada Chan, Shaun Fallat, Steve Kirkland +3
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex…
Strongly chordal digraphs and -free matrices
Pavol Hell, Cesar Hernandez-Cruz, Jing Huang +1
We define strongly chordal digraphs, which generalize strongly chordal graphs and chordal bipartite graphs, and are included in the class of chordal digraphs. They correspond to sq…
The strong spectral property for graphs
Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc
We introduce the set of all simple graphs with the property that each symmetric matrix corresponding to a graph has the st…