Let 􀀀 be a graph whose each vertex is colored either white or black. If u is a black vertex of 􀀀 such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a graph 􀀀 is a subset of vertices Z  V (􀀀 ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the color of all vertices in 􀀀 to black. The zero forcing number of 􀀀 is the minimum of jZj over all zero forcing sets for 􀀀 and is denoted by Z(􀀀 )...

In this article we study the zero forcing number of Generalized Sierpi nski graphs S(G; t). More precisely, we obtain a general lower bound on the zero forcing number of S(G; t) and we show that this bound is tight. In particular, we consider the cases in which the base graph G is a star, path, a cycle or a complete graph.

The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate di erent mathematical structures. Through searching out some properties of one of these structures, we try to  nd some new properties of the other structure as well. This will result in obtaining some unknown properties. At  rst, a novel automaton called zero-forcing (Z-F)  nite automata is de ned according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F- nite automata will be obtained. In addition, the language and the closure properties of Z-F- nite automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F- nite automata are presented. Further, it is shown that there is not any  nite graph such that f be a part of the language of its Z-F- nite automata. Actually, it is proved that for every given graph, the Z-F- nite automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F- nite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

The zero forcing number Z(G) of a graph G is the minimum cardinality of a set S with colored (black) vertices which forces the set V (G) to be colored (black) after some times. \color change rule": a white vertex is changed to a black vertex when it is the only white neighbor of a black vertex. In this case, we say that the black vertex forces the white vertex. We investigate here the concept of connected zero forcing set and connected zero forcing number. We discusses this subject for special graphs and some products of graphs. Also we introduce the connected propagation time. Graphs with extreme minimum connected propagation times and maximum propagation times |G| -1 and |G| -2 are characterized.

Background and Objectives: Design of low-complexity receiver for spacetime block coded (STBC) transmission over multiple-input multiple-output (MIMO) multiple-access channels has been subject of interest over the years. In this regard, zero-forcing receiver, as a low complexity receiver needing as many receive antennas as the numbers of users, has received increasing attention. Methods: This paper investigates multiuser detection for STBC transmission over a flat-fading MIMO multiple-access channel consisting of J co-channel users each with N antennas and a zero-forcing coherent receiver equipping with M receiving antennas. For the cases in which M  J, it was previously claimed that it is impossible to extend this receiver to general scenarios of orthogonal STBC transmission with J  2 and N  2. Results: We provide a theorem allowing this extension to any scenarios satisfying the theorem condition. Describing in more details, we first prove that zero-forcing receiver of M  J antennas can successfully extend to any STBC transmission over MIMO multiple-access systems which provides an Alamouti-like structure for the inner product of equivalent channels between different receive antennas and users. Then, in order to gain more insight, the theorem role on extending zero-forcing receiver for transmission of orthogonal STBC over MIMO multiple-access systems with J  2 and N  2, and also to other STBC schemes like generalized coordinate interleaved orthogonal design and Quasi-orthogonal STBC is investigated in more details. Finally, the average symbol error rate of considered scenarios are numerically evaluated and compered for different STBC schemes with various numbers of J and N. Conclusion: Generally speaking, it is concluded that extension of zero-forcing receiver to any scenarios of OSTBC transmissions over MIMO multiple-access channels exactly depends on satisfaction of the provided theorem and this receiver can be successfully employed in all scenarios providing an Alamoutilike structure for the inner product of equivalent channels between different receiving antennas and users.

A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum k-flow if the absolute values of edges are less than k. We define the zero-sum flow number of G as the least integer k for which G admitting a zero sum k-flow.? ? In this paper we gave complete zero-sum flow and zero sum numbers for categorical and strong product of two graphs namely cycle and paths.

Background: The present study was conducted to know about the association between amount of smoking and mental health plus demographic factors in the Iranian adolescents.Methods: Data of this research was drawn from the National Health Survey in Iran from April 1999-March 2000. All 1745 adolescents aged 15-20 yr that were residence in the eight northwest provinces of Iran, were included in this study. In order to evident zero-inflation and because of sampling design, multilevel zero-inflated Poisson (ZIP) regression applied for analysis of data. We analyzed data with programs written with s-plus. Results: zero-inflated part of ZIP model shows that gender of female effects to increase the chance of "not to smoke cigarette at all" (P< 0.001) and older adolescents are less at risk of smoking than younger (P= 0.036). It also shows that, unemployed (P= 0.028) and Housewife (P= 0. 003), adolescents are more at risk of smoking compare with student adolescents. Under Poisson part of this model, depression (P= 0.012) and gender of female (P< 0.001) are indirectly associated with number of cigarette smoked per day by adolescents.Conclusion: Among adolescent smokers, males smoke more number of cigarettes than females, younger teenager is more at risk of being a smoker than older ones and dropping out of high school is an important risk factor for smoking. We did not find any relation between mental disorders and being a smoker while we did for the relation between number of Smoked Cigarette (NSC) and depression.