On invo-t-clean graph over the ring of integers modulo p

Abstract

In this paper, we introduce and study the involution-t-clean Graph   defined over the ring of integers modulo  , where   is a prime number. The vertex set of   is  , and two distinct vertices   and   are adjacent if and only if  , where  denotes the set of invo-t-clean elements in  . The  is connected, and each vertex has a degree of either four or five. Using this characterization, we investigate several fundamental graph-theoretic properties. Our main result determines the exact diameter .