The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of GRAPHs. We seek to prove that the information ratio of PRISM GRAPHs Yn are equal to 7/4 for any n³5, and we will gave a partial answer to a question of Csirmaz [10]. We will also study the information ratio of two other families Cm×Cn and Pm×Cn and obtain the exact value of information ratio of these GRAPHs.

Let G be a (p; q) GRAPH. Let f: V (G)! f1; 2; : : :; kg be a map where k 2 N and k > 1. For each edge uv, assign the label gcd(f(u); f(v)). f is called k-Total prime cordial labeling of G if jtf (i) 􀀀 tf (j)j  1, i; j 2 f1; 2;


; kg where tf (x) denotes the total number of vertices and the edges labelled with x. A GRAPH with a k-total prime cordial labeling is called k-total prime cordial GRAPH. In this paper we investigate the 4-total prime cordial labeling of some GRAPHs like PRISM, Helm, Dumbbell GRAPH, Sun ower GRAPH.

The Merrifield-Simmons index of a GRAPH is defined as the total number of the independent sets of the GRAPH and the Hosoya index of a GRAPH is defined as the total number of the matchings of the GRAPH. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two GRAPHs K2×H, where H is a path GRAPH Pn, cyclic GRAPH Cn, or star GRAPH Sn, with n vertices (These are called: ladder GRAPH, PRISM GRAPH, and book GRAPH).

In this paper, we enumerate the parameter matrices of all perfect 2-colorings of the generalized PRISM GRAPH Cn × C3, where n ≥ 3,. We also present some generalized results for Cn × Cm, where m, n ≥ 3.

Iran and China relationship goes back to past centuries, even before Islam. But, after the victory of Islam, stronger bonds were developed between the two countries and, gradually, different depictions of Chinese culture and civilization were reflected in Persian literature and particularly in poetry. Chinese religion and ritual, aestheticism, handicrafts and painting are some of the representations to which this essay is devoted. This essay also investigates the general reflection of China in Persian poetry.

The zero forcing number of a GRAPH is the minimum cardinality among all the zero forcing sets of a GRAPH $G$.  The aim of this article is to compute the zero forcing number of complementary PRISM GRAPHs.  Some bounds on the zero forcing number of complementary PRISM GRAPHs are presented. The remainder of this article discusses the following result.  Let $G$ and $\overline{G }$ be connected GRAPHs. Then $Z(G\overline{G})\leq n-1$ if and only if  there exists two vertices $v_i,v_j \in V(G)$ and $i\neq j$ such that, either $N(v_i) \subseteq N(v_j)$ or $N[v_i] \subseteq N[v_j]$ in $G$.