Let R be a commutative ring with 1. In Biswas et al.(Disc Math Algorithms Appl 11 (1):
1950013, 2019), we introduced a graph G (R) whose vertices are elements of R and two …

Let R be a commutative ring with unity. The co-maximal graph Γ (R) is the graph with vertex
set R and two vertices a and b are adjacent if R a+ R b= R. In this paper, we characterize …

Let R be a finite commutative ring with identity. The co-maximal graph Γ (R) is a graph with
vertices as elements of R, where two distinct vertices a and b are adjacent if and only if Ra+ …

Let $ R $ be a commutative ring with identity $1\neq 0$ which admits atleast two maximal
ideals. In this article, we have studied simple, undirected graph $(\operatorname …

Let R be a commutative ring with identity 1≠ 0. The comaximal ideal graph of R is the
simple, undirected graph whose vertex set is the set of all proper ideals of the ring R not …

In this paper we design a MATLAB program to obtain maximal graphs associated to rings Zn
and compute their energy. This program expresses an intrinsic relationship between the …

CURRICULAM- VITAE Page 1 1 CURRICULAM- VITAE Name DR. SANDEEP ARYA Present
Position: Assistant Professor and Head Institute of Environment and Development Studies …