Isospectbal graphs revisited

Abstract

We have reinvestigated isospectral graphs, in particular graphs of interest in chemistry and physics, starting with a brief review of known results on isospectral and endospectral graphs. This is followed by a closer look at isospectrality and isospectral points and an examination of bond-like quantities in isospectral graphs. Characteristic equations (i.e., the equations the solution of which yields the characteristic polynomials) are then introduced and we show that, whenever the number of different equations is sufficiently large, they characterize individual members of an isospectral group uniquely. We end our presentation by construction of several interesting isospectral graphs previously unknown.