2 citations · 3 across the 9 of their papers we have counts for
9 papers
Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph
Shaun Fallat, Seyed Ahmad Mojallal
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and a…
The Spark of Symmetric Matrices Described by a Graph
Louis Deaett, Shaun Fallat, Veronika Furst +3
We investigate the sparsity of null vectors of real symmetric matrices whose off-diagonal pattern of zero and nonzero entries is described by the adjacencies of a graph. We use the…
The -Analogue of Zero Forcing for Certain Families of Graphs
Shaun Fallat, Neha Joshi, Roghayeh Maleki +6
Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a on…
Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +3
For an matrix , let be the number of distinct eigenvalues of . If is a connected graph on vertices, let be the set of all real sy…
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
Sarah Allred, Emelie Curl, Shaun Fallat +4
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently t…
Spectral arbitrariness for trees fails spectacularly
Shaun M. Fallat, H. Tracy Hall, Rupert H. Levene +4
If is a graph and is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph , what can we say about the eigenvalues of all…