ENERGY OF A GRAPH IS NEVER THE SQUARE ROOT OF AN ODD INTEGER

The energy $E(G)$ of a graph $G$ is the sum ofthe absolute values of the eigenvalues of $G$,. {sc Bapat} and {sc Pati}(Bull. Kerala Math. Assoc., {f 1} (2004), 129--132) proved that(a) $E(G)$ is never an odd integer. We now show that (b) $E(G)$ isnever the square root of an odd integer. Furthermore, if $r$ and$s$ are integers such that $r geq 1$ and $0 leq s leq r-1$ and$q$ is an odd integer,vspace{.5mm} then $E(G)$ cannot be of the form $left(2^s,q ight)^{1/r}$,, a result that implies both (a) and (b) asspecial cases.