# Global Signed Domination in Graphs

## Related Articles

- Smarandachely Bondage Number of a Graph. Ebadi, Karam; Pushpalatha, L. // International Journal of Mathematical Combinatorics;Jan2010, Vol. 4, p9
A dominating set D of a graph G is called a Smarandachely dominating s-set if for an integer s, each vertex v in V - D is adjacent to a vertex u Ïµ D such that degu + s = degv. The minimum cardinality of Smarandachely dominating s-set in a graph G is called the Smarandachely dominating...

- Domination Number in 4-Regular Graphs. Ahangar, H. Abdollahzadeh; Pushpalatha, L. // International Journal of Mathematical Combinatorics;Jan2010, Vol. 4, p20
A set of vertices S in a graph G is said to be a Smarandachely k-dominating set if each vertex of G is dominated by at least k vertices of S. Particularly, if k = 1, such a set is called a dominating set of G. The Smarandachely k-domination number Î³k(G) of G is the minimum cardinality of a...

- Colourings in Bipartite Graphs. Venkatakrishnan, Y.B.; V.Swaminathan // International Journal of Computer Applications;Jul2011, Vol. 25, p1
The concept of X-chromatic partition and hyper independent chromatic partition of bipartite graphs were introduced by Stephen Hedetniemi and Renu Laskar. We find the bounds for X-chromatic number and hyper independent chromatic number of a bipartite graph. The existence of bipartite graph with...

- Majority neighborhood number of a graph. Manora, J. Joseline; Swaminathan, V. // Scientia Magna;2010, Vol. 6 Issue 2, p20
A majority neighborhood set of a graph G is defined and the majority neighborhood number is determined for certain standard graphs. Moreover, majority vertex cover of G and its number are surveyed. Also certain relationships with these parameters of G are investigated.

- STRUCTURE OF THE SET OF ALL MINIMAL TOTAL DOMINATING FUNCTIONS OF SOME CLASSES OF GRAPHS. Kumar, K. Reji; MacGillivray, Gary // Discussiones Mathematicae: Graph Theory;2010, Vol. 30 Issue 3, p407
In this paper we study some of the structural properties of the set of all minimal total dominating functions (FT ) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph....

- A CHARACTERIZATION OF (yt, y2)-TREES. You Lu; Xinmin Hou; Jun-Ming Xu; Ning Li // Discussiones Mathematicae: Graph Theory;2010, Vol. 30 Issue 3, p425
Let ?t(G) and ?2(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: ?t(T) ? ?2(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

- Total Domination in Partitioned Graphs. Frendrup, Allan; Vestergaard, Preben Dahl; Yeo, Anders // Graphs & Combinatorics;May2009, Vol. 25 Issue 2, p181
We present results on total domination in a partitioned graph G = ( V, E). Let ? t( G) denote the total dominating number of G. For a partition $$V_1, V_2, \ldots , V_k$$, k = 2, of V, let ? t( G; V i) be the cardinality of a smallest subset of V such that every vertex of V i has a neighbour in...

- EFFICIENT (j; k)-DOMINATION. Rubalcaba, Robert R.; Slater, Peter J. // Discussiones Mathematicae: Graph Theory;2007, Vol. 27 Issue 3, p409
A dominating set S of a graph G is called efficient if |N[?] nS| = 1 for every vertex ? ... V(G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple...

- ON THE (2; 2)-DOMINATION NUMBER OF TREES. You Lu; Xinmin Hou; Jun-Ming Xu // Discussiones Mathematicae: Graph Theory;2010, Vol. 30 Issue 2, p185
Let Î³(G) and Î³2;2(G) denote the domination number and (2; 2)-domination number of a graph G, respectively. In this paper, for any nontrivial tree T, we show that (2Î³(T)+1)/3 ≤ â‰¤2;2(T) â‰¤ 2(T). More-over, we characterize all the trees achieving the equalities.