For any graph G a set D of vertices of G is a dominating set, if every vertex v∈V (G)− D has at least one neighbor in D. The domination number (G) is the smallest number of vertices in any dominating set. In this paper, a characterization is given for block graphs having a unique minimum dominating set. With this result, we generalize a theorem of Gunther, Hartnell, Markus and Rall for trees. c...

From the study of X-ray light curve and color-color diagram of the low mass X-ray binary GRS 1915+105, observed by on board proportional counter array (PCA) of Rossi X-ray Timing Explorer (RXTE), we discover a new class of variability, which we name ǫ class. We have studied observations between MJD 51200 and 51450. The class shows unusual periodic-like variation in count rate during rise time o...

A number of optimization methods require as a rst step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an in nite number of) convex functions, and we show how to o...

A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdiv...

A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...

Let be a simple undirected fuzzy graph. A subset S of V is called a dominating set in G if every vertex in V-S is effectively adjacent to at least one vertex in S. A dominating set S of V is said to be a Independent dominating set if no two vertex in S is adjacent. The independent domination number of a fuzzy graph is denoted by (G) which is the smallest cardinality of a independent dominating ...

A signed Roman dominating function (SRDF) on a graph G is a function f : V (G) → {−1, 1, 2} such that u∈N [v] f(u) ≥ 1 for every v ∈ V (G), and every vertex u ∈ V (G) for which f(u) = −1 is adjacent to at least one vertex w for which f(w) = 2. A set {f1, f2, . . . , fd} of distinct signed Roman dominating functions on G with the property that ∑d i=1 fi(v) ≤ 1 for each v ∈ V (G), is called a sig...

A dominating set of a graph G = (V,E) is a subset D of V such that every vertex of V − D is adjacent to a vertex in D. In this paper we introduce a generalization of domination as follows. For graphs G and H, an H-matching M of G is a subgraph of G such that all components of M are isomorphic to H. An H-dominating matching of G is a Hmatching D of G such that for each x ∈ V (G) there exists y ∈...

Let f = ∑ n≥1 λf (n)n (k1−1)/2qn and g = ∑ n≥1 λg(n)n (k2−1)/2qn be two newforms with real Fourier coeffcients. If f and g do not have complex multiplication and are not related by a character twist, we prove that #{n ≤ x | λf (n) > λg(n)} x.