11 papers · 1 filter
Maximum spectral sum of graphs
Hitesh Kumar, Lele Liu, Hermie Monterde +2
For a graph of order , the spectral sum of is defined to be the sum , where (resp. ) is the largest (resp. second largest) adjacency ei…
Laplacian state transfer in graphs with involutions
Swornalata Ojha, Hermie Monterde, Hiranmoy Pal
For , the generalized Laplacian of a graph is the matrix , where is the degree matrix and is the adjacency matrix of $X…
Local -uniform mixing in continuous quantum walks
Hermie Monterde
Let be a weighted graph and be its adjacency, Laplacian or signless Laplacian matrix. In a continuous quantum walk on , local -uniform mixing occurs at vertex if…
Sedentary quantum walks on bipartite graphs
Karen Meagher, Hermie Monterde
If a quantum walk starting on a vertex tends to stay at home, then that vertex is said to be sedentary. We prove that almost all planar graphs and almost all trees contain at least…
Structured eigenbases and pair state transfer on threshold graphs
Leonardo de Lima, Renata Del-Vecchio, Hermie Monterde +1
Recently, Macharete, Del-Vecchio, Teixeira and de Lima showed that a star and any threshold graph on the same number of vertices share the same eigenbasis relative to the Laplacian…
Quantum walks on finite and bounded infinite graphs
Chris Godsil, Steve Kirkland, Sarojini Mohapatra +2
A weighted graph with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in . I…