Families of Integral Cographs within a Triangular Array

Abstract

The determinant Hosoya triangle, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle mod 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.

Keywords

• fibonacci number
• determinant hosoya triangle
• adjacency matrix
• eigenvalue
• integral graph
• cograph
• primary 68r11
• secondary 11b39