Measuring the similarity of spectra of molecular graphs

Abstract

Three measures of the similarity of the spectra of molecular graphs are considered. Two of them are previously known: the "almost-isospectrality measure", <i>aim, </i>and the "angle of isomerization", <i>ais. </i> We now introduce a third such quantity-the "vectorial isospectrality measure", <i>vim. </i> The previous definitions of <i>aim </i>and <i>ais </i> are modified so as to make them applicable to arbitrary pairs of molecular graphs with equal number of vertices. We establish relations between <i>aim, ais </i> &amp; <i>vim, </i> and point out some of their other properties.