planarity of the intersection graph. Also, among the other things, we show that if the

clique number of G(P) is finite, then P is finite too....

the

clique number and automorphism group of n

R, where R = Zp^2 or R = Zp^3 ....

. In the first proposed formulation, we use an idea based on the formulation of the classical control project problem. In the second formulation, we try to insert the clique constraints to the model....

,graph height, Wiener index and clique number. Moreover, we study the Hasse ideal digraph HT(R), which is a spanning subgraph of IT(R) such that for each two distinct vertices I and J, there is an arc from I to J in HT(R) whenever I -J in IT...

and J are adjacent whenever

I + K = J or J + K = I, for some ideal K in S . In this paper, we study some basic properties of the graphs

Cay^-(I(R); S ) and Cay^+(I(R); S ) such as connectivity, girth and clique number. Moreover, we...

Let R be a Noetherian commutative ring. The regular digraph of ideals of

R introduced in [10] which denoted by

−−→

Γreg(R). The vertex set of

−−→

Γreg(R) is set of

nontrivial ideals ...

except the case that |X|= 2 and n = 1. Also we investigate the clique number of G_n R. Moreover we obtain a

suitable bound for the independence number of G_n R....

In this paper, for a bounded lattice L and an ideal I of L, we introduce the

zero-divisor graph of L with respect to I , denoted by T-I (L). We study the interplay

of lattice-theoretic properties of L with ...