ENERGY OF SIGNED UNIT GRAPHS

Abstract

In this paper, the authors determine the energy of signed unit graphs $G_{\Sigma}(R)$ associated with finite commutative ring $R$. We establish sufficient conditions under which the energy of $G_{\Sigma}(R)$ equals the number of vertices of the graph. Moreover, it has been shown that for all local rings, the energies of the signed and underlying unit graphs are same. Furthermore, it has been shown that when a ring is isomorphic to a finite product of copies of $\mathbb{Z}_2$, the energy of its signed unit graph equals the order of the ring.