The prime ideal sum graph of a commutative unital ring R, denoted by PIS (R), is an undirect
and simple graph whose vertices are nontrivial ideals of R and there exists an edge …

The concept of metric-related parameters permeates all of graph theory and plays an
important role in diverse networks, such as social networks, computer networks, biological …

Consider a commutative ring with unity denoted as R. An ideal I of a ring R is called an
annihilating ideal if there exists a non-zero element r∈ R such that rI= 0. An ideal J of R is …

The annihilator graph $ AG (R) $ of the commutative ring $ R $ is an undirected graph with
vertex set as the set of all non-zero zero divisors of $ R $, and two distinct vertices $ x $ and …

Let R be a commutative ring with identity and A (R) be the set of ideals with non-zero
annihilator. The annihilator-ideal graph of R is defined as the graph AI (R) with the vertex set …

Let S be the smallest subset of vertices in a graph G such that every vertex outside of S has
a unique distance vector with respect to S. Then| S| is defined as the metric dimension of G …

The strongly annihilating-ideal graph SAG (R) of a commutative unital ring R is a simple
graph whose vertices are non-zero ideals of R with non-zero annihilator and there exists an …

For a connected graph G (V, E) a clique S⊆ V (G) is twin-free if every pair of elements of S
have distinct closed neighborhoods and the number of elements in a twin-free clique of …

Let R be a commutative ring with identity. The annihilator graph AG (R) is a simple graph
with vertex set as the set of all non-zero zero-divisors of R, and two distinct vertices a and b …