Unit graph of type - 2

Abstract

The unit graph of ring R was introduced in commutative rings by Vasantha Kandasamy[27]. In this short note, we introduce the concept namely “Unit graph of type-2” denoted by UG2(R) in associative rings R and announced a few important fundamental results. In section 3, we prove that the number of edges in the unit graph of type-2 of Zp is p – 3/2. In section 4, we prove that sum of the degrees of the vertices in UG2(R) is equal to (|U(R)|−number of self units). Also we have included some examples.