2020/09/06 by Ching, Hsin-Yun, Flórez, Rigoberto, Mukherjee, Antara
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2009.02770
The determinant Hosoya triangle, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle \bmod 2 gives rise to three infinite families of graphs, that are formed by complete product (join) of (the union of) two complete graphs with an empty graph. We give a necessary and sufficient condition for a graph from these families to be integral. Some features of these graphs are: they are integral cographs, all graphs have at most five distinct eigenvalues, all graphs are either d-regular graphs with d=2,4,6,… or almost-regular graphs, and some of them are Laplacian integral. Finally we extend some of these results to the Hosoya triangle.