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 R be a commutative ring with identity and I∗(R), the set of all nontrivial proper ideals of
R. The intersection graph of ideals of R, denoted by ℐ (R), is a simple undirected graph with …

Let R be a commutative ring with identity and Nil (R) be the set of nilpotent elements of R.
The nil-graph of ideals of R is defined as the graph AG N (R) whose vertex set is {I:(0)≠ I⊲ …

CAYLEY SUM GRAPHS OF IDEALS OF A COMMUTATIVE RING Page 1 J. Aust. Math. Soc. 96
(2014), 289–302 doi:10.1017/S144678871400007X CAYLEY SUM GRAPHS OF IDEALS OF …

A rectangular band is defined as a direct product of a left zero semigroup and a right zero
semigroup, and a rectangular group is defined as a direct product of a group and a …

Let G be a group and let S be a subset of G\{e} with S-1⊆ S, where e is the identity element
of G. The Cayley graph Cay (G, S) is a graph whose vertices are the elements of G and two …

Let V be a finite dimensional vector space over the field F. Let S(V) be the set of all
subspaces of V and A⊆S^*(V)=S(V)\{0\}. In this paper, we define the Cayley subspace sum …

Let R be a commutative ring, ℐ (R) the set of all ideals of R and S, a subset of ℐ∗(R)= ℐ
(R)\{0}. The Cayley sum graph of ideals of R, denoted by Cay (ℐ (R), S), is a simple …

A cyclic edge-cut of a graph G is an edge set, the removal of which separates two cycles. If G
has a cyclic edge-cut, then it is said to be cyclically separable. For a cyclically separable …

Abstract‎ Let $ R $ be a finite ring (with non-zero identity) and let $ Bi (G_ {R}), $ denote the
unitary one-matching bi-Caylay graph over $ R. $ In this paper‎,‎ we calculate the chromatic‎,‎ …