In this work, we study the signed Roman domination number of the join of graphs. Specially, we determine it for the join of cycles, wheels, fans, and friendship graphs.

Let G = (V,E) be a simple and undirected graph. For some integer k > 1, a set D ⊆ V is said to be a k-dominating set in G if every vertex v of G outside D has at least k neighbors in D. Furthermore, for some real number α with 0 < α 6 1, a set D ⊆ V is called an α-dominating set in G if every vertex v of G outside D has at least α×dv neighbors in D, where dv is the degree of v in G. The cardina...

A set D ⊆ V of vertices is said to be a (connected) distance k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in G is the (connected) distance k-domination number of G, denoted by γk(G) (γ c k (G), respectively). The set D is defined to be a total k-do...

Let S be a dataset of n 2-dimensional points. The top-k dominating query aims to report the k points that dominate the most points in S . A point p dominates a point q iff all coordinates of p are smaller than or equal to those of q and at least one of them is strictly smaller. The top-k dominating query combines the dominance concept of maxima queries with the ranking function of top-k queries...

A subset S of a vertex set of a graphG is a total (k, r)-dominating set if every vertex u ∈ V (G) is within distance k of at least r vertices in S. The minimum cardinality among all total (k, r)-dominating sets ofG is called the total (k, r)domination number of G, denoted by γ (k,r)(G). We previously gave an upper bound on γ t (2,r)(G(n, p)) in random graphs with non-fixed p ∈ (0, 1). In this p...

A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = k n = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found then the conception of k-domina...

Efficient routing among mobile hosts is an important function in ad hoc networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts are either in the set or neighbors of hosts in the set. The efficiency of dominating-set-based routing mainly depends on the overhead intr...

In standard kernelization algorithms, the usual goal is to reduce, in polynomial time, an instance (I, k) of a parameterized problem to an equivalent instance (I ′, k′) of size bounded by a function in k. One of the central problems in this area, whose investigation has led to the development of many kernelization techniques, is the Dominating Set problem. Given a graph G and k ∈ N, Dominating ...

We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13–28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the rôle of circuits is taken over by signed circuits of a signed graph which are known to occur in two types – either balanced circuits or pairs of disjoint unbalanced circuits connecte...