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20212026
most citedStrong Cospectrality and Twin Vertices in Weighted Graphs

10 citations · 32 across the 19 of their papers we have counts for

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8 papers · 1 filter

math.CO2026

Quantum walks and graph operations

Joy Cooper, Homer De Vera, Hermie Monterde +3

Let be the transition matrix of a quantum walk on a graph relative to its adjacency matrix or the Laplacian matrix . This paper investigates the behavior of qua…

math.CO2026

Near-factorizations in association schemes

Allen Herman, Alice Lacaze-Masmonteil, Karen Meagher +1

We formally initiate the study of -fold near-factorizations in association schemes. Namely, given an association , we consider the existence of a facto…

quant-ph2026

Perfect -state transfer

Stephen Kirkland, Hermie Monterde, Sarah Plosker

Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirec…

math.CO2026

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…

math.CO2026

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…

math.CO2026

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…

math.CO2026

Sedentary quantum walks on bipartite and planar 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…

math.CO2026

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…