In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

Let V be a left R-module where R is a (not necessarily commutative) ring with unit. The
intersection graph of proper R-submodules of V is an undirected graph without loops and …

For a nontrivial finite group G, the intersection graph Γ (G) of G is the simple undirected
graph whose vertices are the nontrivial proper subgroups of G and two vertices are joined by …

Let G be a group. The intersection graph of G, denoted by Γ (G), is the graph whose vertex
set is the set of all nontrivial proper subgroups of G and two distinct vertices H and K are …

Let U be a left R-module where R is a commutative ring with identity. The maximal
submodule graph MG (U) of proper R-submodules of U is an undirected graph defined as …

Let R be a commutative semiring with identity, and U be a unitary left R-semimodule. The
small intersection graph of nontrivial subsemimodules of U, denoted by Γ (U), is an …

In this paper, a new kind of graph on a commutative ring is introduced and investigated.
Small intersection graph of a ring $ R $, denoted by $ G (R) $, is a graph with all non-small …

Let R be a commutative ring with identity. The intersection graph of ideals of a ring R is an
undirected simple graph denoted by Γ (R) whose vertices are in a one-to-one …

Abstract Let\(M\) be a unitary left\(R\)-module where\(R\) is a ring with identity. The co-
intersection graph of proper submodules of\(M\), denoted by\(\Omega (M)\), is an undirected …

Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of,
denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and …