On Numerical Characterization of Cyclicity

We propose characterizing the cyclicity of molecular graphs by considering their D/DD matrix. Each nondiagonal element of D/DD is a quotient of the corresponding elements of the distance matrix D and the detour matrix DD of a graph. In particular, we are using the leading eigenvalue of the D/DD matrix as a descriptor of cyclicity and are investigating for monocyclic graphs Cn how this eigenvalue depends on the number of vertexes n, as n approaches infinity.