The purpose of this paper is to appl y of concept of fuzzy bridge and to ex tend of notation of fuzzy domination Number in fuzzy graph. F uzzy bridge introduces a new notation of fuzzy domination sets and fuzzy domination Numbers such that is consedering for fuzzy graphs with cyclics and vertices are l ocated on cyclics. To check the importance of fuzzy domination Numbers based on fuzzy bridge, we compare it to other distinct fuzzy domination Numbers and show that fuzzy domination Numbers based on fuzzy bridge is optimal. The main method, in this research is based on computations of fuzzy domination Number of complete fuzzy graphs with distinct fuzzy vertices and is worked on spec ial and useful fuzzy graphs such as st rong 2-wh eel fuzzy graph and 2-complet e fuzzy graph. The study on 2-wh eel fuzzy graph and 2-complet e fuzzy graph was given for the first time in this paper and are worked via the generalize of 2-part of wh eel fuzzy graph and complet e fuzzy graph which these special fuzzy graphs have many applications on complex networks. In this study, computations of fuzzy domination Number of special fuzzy graphs are done based on fuzzy bridge with distinct vertices. The paper includes implications for the development of fuzzy graph, and for modeling the uncertainty problems and applicaions in real world which we consider t wo modes of real problems.

In this paper we investigate the Color:rgb(255,0,120);">Dominating--Color Number، of a graph G. That is the maximum Number of Color classes that are also Color:rgb(255,0,120);">Dominating when G is Colored using Colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].

A set S of vertices in a graph G is a Color:rgb(255,0,120);">Dominating set if every vertex of V-S is adjacent to some vertex in S. The domination Number g (G) is the minimum cardinality of a Color:rgb(255,0,120);">Dominating set in G. The annihilation Number a (G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the Number of edges in G. In this paper, we show that for any tree T of order n³2, g (T)£3a (T)+2/4, and we characterize the trees achieving this bound.

In this paper, the concept of incidence domination Number of graphs is introduced and the incidence Color:rgb(255,0,120);">Dominating set and the incidence domination Number of some particular graphs such as paths, cycles, wheels, complete graphs and stars are studied.

Any human group enjoying a structure and organization, consider itself a mission, either explicity or implicitly. This mission or the goals of the organization may sometimes be mentioned. in the consitution of the organization. In Post Renaissance period, especially after the Industrial Revolution, modem universities were created. They set a mission and a Number of objectives for themselves, some of which are known by the public and some others, usually the most important and the political ones, only by the intellectual elites. Setting goals and objectives is not specific to western universities. The same is also true for other groups and organizations, including political parties. It is believed that underlying any structure is an ideology. The present article tries to study and analyze the ideologies Color:rgb(255,0,120);">Dominating the Iranian geography from the beginning to the present; that is, from the creation of geography department at Tehran university up to now. Being the first attempt in this domain, the author maintains that there are some deficiencies in the article and needs more elaboration and analysis in future attempts.

Let be a simple and undirected graph with vertex set. A set is called a Color:rgb(255,0,120);">Dominating set of if every vertex outside is adjacent to at least one vertex of. For any integer, a Color:rgb(255,0,120);">Dominating set is called a-adjacency Color:rgb(255,0,120);">Dominating set of if the induced subgraph contains at least one vertex of degree at most. The minimum cardinality of a-adjacency Color:rgb(255,0,120);">Dominating set of is called the-adjacency domination Number of that is denoted by. In this paper, the study of-adjacency domination in graphs is initiated, and exact values and some bounds on the-adjacency domination Number of a given graph are presented. Furthermore, it is shown that there is a polynomial-time algorithm that computes the-adjacency domination Number of a given tree. Moreover, it is proven that the decision problem associated to the-adjacency domination is NP-complete for bipartite graphs.

In this paper, we dene the common minimal Color:rgb(255,0,120);">Dominating signed graph of a given signed graph and offer a structural characterization of common minimal Color:rgb(255,0,120);">Dominating signed graphs. In the sequel, we also obtained switching equivalence characterizations: S¯ ~ CMD (S) and CMD(S) ~ N (S), where S¯, CMD (S) and N (S) are complementary signed graph, common minimal signed graph and neighborhood signed graph of S respectively.

A graph $G$ is called semi square stable if $\alpha (G^{2})=i(G)$ where $%\alpha (G^{2})$ is the independence Number of $G^{2}$ and $i(G)$ is the independent Color:rgb(255,0,120);">Dominating Number of $G$. A subset $S$ of the vertex set of a graph $G$ is an efficient Color:rgb(255,0,120);">Dominating set if $S$ is an independent set and every vertex of $G$ is either in $S$ or adjacent to exactly one vertex of $%S. $ In this paper, we show that every square stable graph has an efficient Color:rgb(255,0,120);">Dominating set and if a graph has an efficient Color:rgb(255,0,120);">Dominating set, then it is semi square stable. We characterize when the join and the corona product of two disjoint graphs are semi square sable graphs and when they have efficient Color:rgb(255,0,120);">Dominating sets.