2 papers
math.CO2024
A bound on the girth of quaternion unit gain graphs in terms of the rank
Suliman Khan, Edwin R. van Dam
We obtain a bound on the girth g of a quaternion unit gain graph in terms of the rank r of its adjacency matrix. In particular, we show that g <= r + 2 and characterize all quatern…
math.CO2024
Gain distance Laplacian matrices for complex unit gain graphs
Suliman Khan
A complex unit gain graph (or a -gain graph) is a graph where the unit complex number is assign by a function to every oriented edge of and assign its…