In this talk we provide a generalization of Cayley graphs for commutative ring. Our result provide extensions of some theorems in unit and unitary Cayley graphs.‎...

an n × n lower triangular matrix A over R whose entries on

the main diagonal are non-zero such that AX^t = Y t or AY^ t = Xt, where,

for a matrix B, B^t is the matrix transpose of B. T^n

R is a generalization of Cayley graph. Let T...

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an nxn lover triangular matrix over R whose entries on the main diagonal are non-zero such that AX^T=Y^T or‎

AY^T=X^T. When we consider the ring R with multiplication as a semigroup, the T^1R is the usual undirected cayley graph. In this note we...

define G(R,G, S) to be the graph with vertex set R

and two distinct elements x, y R are adjacent if and only if there exists s

such that x + sy This graph provides a generalization of the unit and unitary

Cayley graphs....

In this paper, we introduce and study a new class of Cayley graphs....

Let R be a commutative ring with unity and R+, U and U∗ be the additive

group, multiplicative prime subset of R and U\\\\{0}. We denote by Cay(R)

the cayley graph Cay(R+,U^*). In this paper, we investigate the structure of Cay(R)....

-zero diagonal entries such that AX^T = Y ^T or AY^ T = X^T. By

B^T , we mean transpose of matrix B. If R is a semigroup with respect to multiplication and

n = 1, then T^1_R is the undirected Cayley graph. In this paper, a prime number p, we find...

‎Let L be a lattice. For a natural number n we associate a simple graph denoted by T^nL with L^n-{0} as the vertex set and two distinct vertices X and Y begin adjacent if and only if there exists an nxn lower triangular ...

the ring R as a semigroup with

respect to multiplication, then Gamma^1_R is the usual

undirected Cayley graph (over a semigroup). Hence Gamma^n_R is

a generalization of Cayley graph. In this paper we study some

basic properties...

Abstract. The relative Cayley graph of a group G with respect to its proper subgroup H, is a graph whose vertices are elements of G and two vertices h ∈ H and g ∈ G are adjacent if g = hc for some c ∈ C, where C is an inverse-closed subset of G. We...