A graph is k-connected if it has k internally-disjoint paths between every pair of nodes. A subset S of nodes in a graph G is a kconnected set if the subgraph G[S] induced by S is k-connected; S is an m-dominating set if every v ∈ V \ S has at least m neighbors in S. If S is both k-connected and m-dominating then S is a k-connected m-dominating set, or (k,m)-cds for short. In the k-Connected mD...

A k-dominating set of a graph G is a subset D of the vertices of G such that every vertex of G is either in D or at distance at most k from a vertex in D. It is of interest to find k-dominating sets of small cardinality. In this paper we consider simple randomised greedy algorithms for finding small k-dominating sets of regular graphs. We analyse the average-case performance of the most efficie...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

Let G = (V, E) be a graph without isolated vertices. A set D ⊆ V is a d-distance paired-dominating set of G if D is a d-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a d-distance paired-dominating set for graph G is the d-distance paired-domination number, denoted by γd p(G). In this paper, we study the ddistance paired-domination n...

We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor. In other words, we give polynomial time algorithms that, for a given H-topological-minor free graph G and a positive integer k, output an H-topological-minor free graph G′ on O(k) vertices such that G has a (connected) dominating set of size k if ...

During the formation of the metaphase spindle in animal somatic cells, kinetochore microtubule bundles (K fibers) are often disconnected from centrosomes, because they are released from centrosomes or directly generated from chromosomes. To create the tightly focused, diamond-shaped appearance of the bipolar spindle, K fibers need to be interconnected with centrosomal microtubules (C-MTs) by mi...

The top-k dominating query returns the k database objects with the highest score with respect to their dominance score. The dominance score of an object p is simply the number of objects dominated by p, based on minimization or maximization preferences on the attribute values. Each object (tuple) is represented as a point in a multidimensional space, and therefore, the number of attributes equa...

Kamei and Kakugawa have recently proposed a self-stabilizing algorithm for the minimal k-dominating set problem. Their algorithm is a general form of the maximalindependent-set algorithm proposed by Shukla et al. The results in their paper are for any tree network that assumes Dijkstra’s central demon model. In particular, the worstcase stabilization time is claimed to be O(n), where n is the n...

Let k be a positive integer and G = (V,E) be a simple graph. A subset S ⊆ V is dominating in G, if for each vertex v ∈ V \ S, N(v) ∩ S 6= ∅. In 1985, Fink and Jacobson gave a generalization of the concept of dominating sets in graphs. A subset S of V is kdominating in G, if every vertex of V \ S is adjacent to at least k vertices in S. In this paper, we characterize vertices that are in all or ...