-Consistency in signed total graphs of commutative rings.

Motivated by the earlier study on the notion of signed total graph of a commutative ring, in this paper, we characterize all the commutative rings with unity for which signed total graph is -consistent and sign-compatible. To do this, first, we derive a formula to determine the degree of each vertex in (induced subgraph of the total graph), when and , where each 's is a field of characteristic , is an odd prime, and . [ABSTRACT FROM AUTHOR]