5 papers
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…