6 citations · 10 across the 14 of their papers we have counts for
15 papers
Claw-free cubic graphs and zero forcing
Jorge Lozano, Shahla Nasserasr, Thomas Wall
A claw-free cubic graph is a cubic graph with no induced subgraph isomorphic to . The zero forcing process begins with an initial set of colored vertices. At each step…
Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +3
The parameter of an -vertex graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . We show that all with $e(\…
Well-forced graphs
Cheryl Grood, Ruth Haas, Bonnie Jacob +2
A graph in which all minimal zero forcing sets are in fact minimum size is called ``well-forced." This paper characterizes well-forced trees and presents an algorithm for determini…
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…
Sparsity of Graphs that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +5
The parameter of a graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . It is shown that the minimum number of edg…
Colourings of -coloured mixed graphs
Gary MacGillivray, Shahla Nasserasr, Feiran Yang
A mixed graph is, informally, an object obtained from a simple undirected graph by choosing an orientation for a subset of its edges. A mixed graph is -coloured if each edg…
Reconfiguration of Colourings and Dominating Sets in Graphs: a Survey
C. M. Mynhardt, S. Nasserasr
We survey results concerning reconfigurations of colourings and dominating sets in graphs. The vertices of the -colouring graph of a graph correspond to…
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…
Achievable multiplicity partitions in the inverse eigenvalue problem of a graph
Mohammad Adm, Shaun Fallat, Karen Meagher +3
Associated to a graph is a set of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the gr…
Rigid linkages and partial zero forcing
Daniela Ferrero, Mary Flagg, H. Tracy Hall +5
Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown t…
Minimum number of distinct eigenvalues of graphs
Bahman Ahmadi, Fatemeh Alinaghipour, Michael S. Cavers +3
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph , is denoted by . Using other parameters related to , b…
The minimum rank of universal adjacency matrices
Bahman Ahmadi, Fatemeh Alinaghipour, Shaun M. Fallat +3
In this paper we introduce a new parameter for a graph called the {\it minimum universal rank}. This parameter is similar to the minimum rank of a graph. For a graph the minimu…