Secure Domination Research Articles

Physiological Regulation of Growth during Social Ascension in a Group-Living Fish.

In social groups, dominant animals typically are larger and have better access to resources than subordinates. When subordinates are given the opportunity to ascend to a dominant position, they will elevate their rates of growth to help secure dominance. This study investigated the physiological mechanisms facilitating this increased growth. Using the group-living cichlid, Neolamprologus pulcher, we investigated whether the insulin-like growth factor (IGF) system-a key regulator of growth-is involved in the regulation of growth during social ascension. We also assessed differences in energy storage and expenditure among dominant, subordinate, and ascending males to determine the energetic costs associated with ascension. Daily growth rates tripled during ascension, and ascending males expended more energy after ascension, owing to higher rates of energetically costly social behaviors, increased locomotor activity, and larger home ranges. Ascenders did not increase food intake to offset increasing energetic costs but had half the liver glycogen energy stores of subordinates. Together, these results indicate a reliance on stockpiled energy reserves to fuel the high energetic demands associated with ascension. Transcript abundance of IGF binding proteins 1 (igfbp1) and 2a (igfbp2a) were low in ascenders relative to subordinates, suggesting a higher capacity for growth during ascension through increased bioavailability of circulating IGF-1. Our findings provide clear evidence of the energetic costs of social ascension and offer novel insight into the physiological mechanisms modulating the social regulation of growth.

A simple algorithm for secure domination in proper interval graphs

In [Secure domination in proper interval graphs, Discrete Applied Mathematics 247 (2018) 70–76], Araki and Miyazaki proposed a linear-time algorithm for finding the secure domination number of proper interval graphs. However, the example they provided is exactly a counterexample. Based on their main idea, we propose a new simple algorithm for solving this problem in this paper.

The secure domination problem in cographs

Let G=(V,E) be a graph. A subset D of vertices of G is called a dominating set of G if for every u∈V∖D, there exists a vertex v∈D such that uv∈E. A dominating set D of a graph G is called a secure dominating set of G if for every u∈V∖D, there exists a vertex v∈D such that uv∈E and (D∖{v})∪{u} is a dominating set of G. The secure domination number of G, denoted by γs(G), is the minimum cardinality of a secure dominating set of G. In this paper, we present an O(n+m) time algorithm to compute the secure domination number of a cograph having n vertices and m edges.

Protection of graphs with emphasis on Cartesian product graphs

In this paper we study the weak Roman domination number and the secure domination number of a graph. In particular, we obtain general bounds on these two parameters and, as a consequence of the study, we derive new inequalities of Nordhaus-Gaddum type involving secure domination and weak Roman domination. Furthermore, the particular case of Cartesian product graphs is considered.

Secure and Efficient Skyline Queries on Encrypted Data.

Outsourcing data and computation to cloud server provides a cost-effective way to support large scale data storage and query processing. However, due to security and privacy concerns, sensitive data (e.g., medical records) need to be protected from the cloud server and other unauthorized users. One approach is to outsource encrypted data to the cloud server and have the cloud server perform query processing on the encrypted data only. It remains a challenging task to support various queries over encrypted data in a secure and efficient way such that the cloud server does not gain any knowledge about the data, query, and query result. In this paper, we study the problem of secure skyline queries over encrypted data. The skyline query is particularly important for multi-criteria decision making but also presents significant challenges due to its complex computations. We propose a fully secure skyline query protocol on data encrypted using semantically-secure encryption. As a key subroutine, we present a new secure dominance protocol, which can be also used as a building block for other queries. Furthermore, we demonstrate two optimizations, data partitioning and lazy merging, to further reduce the computation load. Finally, we provide both serial and parallelized implementations and empirically study the protocols in terms of efficiency and scalability under different parameter settings, verifying the feasibility of our proposed solutions.

Secure Domination in Lict Graphs

Secure Domination in Lict Graphs

Secure domination in proper interval graphs

A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u∉S, there is a vertex v∈S such that uv is an edge and (S∖{v})∪{u} is also a dominating set of G. The secure domination number γs(G) is the cardinality of a smallest secure dominating set of G. In this paper, we propose a linear-time algorithm for finding the secure domination number of proper interval graphs.

The complexity of secure domination problem in graphs

The complexity of secure domination problem in graphs

Complexity Issues of Variants of Secure Domination in Graphs

Let G=(V,E) be a simple, undirected and connected graph. A connected dominating set S⊆V(G) is a secure connected dominating set of G, if for each u∈V(G)\\S, there exists v∈S such that (u,v)∈E(G) and the set (S\\{v})∪{u} is a connected dominating set of G. The minimum cardinality of a secure connected dominating set of G denoted γsc(G), is called the secure connected domination number of G. In this paper, we show that the decision problems of finding a minimum secure connected dominating set and a minimum secure total dominating set are NP-complete for split graphs. We initiate the study of 2-secure domination and show that the decision problem corresponding to the computation of 2-secure domination number of a graph is NP-complete, even when restricted to split graphs or bipartite graphs. Finally we show that given two positive integers k(≥2) and n(≥max⁡{4,k}) there exists a graph G with |V(G)|=n and γsc(G)=k.

On computing a minimum secure dominating set in block graphs

In a graph $$G=(V,E)$$G=(V,E), a set $$D \subseteq V$$D⊆V is said to be a dominating set of G if for every vertex $$u\in V{\setminus }D$$u?V\D, there exists a vertex $$v\in D$$v?D such that $$uv\in E$$uv?E. A secure dominating set of the graph G is a dominating set D of G such that for every $$u\in V{\setminus }D$$u?V\D, there exists a vertex $$v\in D$$v?D such that $$uv\in E$$uv?E and $$(D{\setminus }\{v\})\cup \{u\}$$(D\{v})?{u} is a dominating set of G. Given a graph G and a positive integer k, the secure domination problem is to decide whether G has a secure dominating set of cardinality at most k. The secure domination problem has been shown to be NP-complete for chordal graphs via split graphs and for bipartite graphs. In Liu et al. (in: Proceedings of 27th workshop on combinatorial mathematics and computation theory, 2010), it is asked to find a polynomial time algorithm for computing a minimum secure dominating set in a block graph. In this paper, we answer this by presenting a linear time algorithm to compute a minimum secure dominating set in block graphs. We then strengthen the known NP-completeness of the secure domination problem by showing that the secure domination problem is NP-complete for undirected path graphs and chordal bipartite graphs.

Secure Triple Connected Domination Number of a Graph

Secure domination is a well-studied concept [3, 4, 5]. In this domination, a vertex outside has the chance of coming inside the dominating set by replacing an element of the set without affecting domination. This idea is combined with the concept of triple connected domination, by considering a path between any three vertices of a graph [10, 11, 12], to introduce a new parameter called secure triple connected domination. A secure dominating set \(S\) of \(V\) of a nontrivial graph \(G\) is said to be secure triple connected dominating set, if the induced sub graph \(\langle S\rangle\) is triple connected. Among all the secure triple connected dominating sets of the graph \(G\), a set having the minimum cardinality is called the secure triple connected domination number denoted by \(\gamma_{stc}\) of \(G\). We have determined the exact values of secure triple connected domination number for some standard graphs and obtained bounds for this new parameter. NORDHAUS-GADDUM type results and the relationship of this parameter with other graph theoretical parameters are also discussed.

Disjoint Secure Domination in the Join of Graphs

Let G = (V(G),E(G)) be a simple connected graph. A dominating set S in G is called a secure dominating set in G if for every u ∈ V (G) S, there exists v ∈ S ∩ NG(u) such that (S {v}) ∪ {u} is a dominating set. The minimum cardinality of secure dominating set is called the secure domination number of G and is denoted by γs(G). A secure dominating set of cardinality γs(G) is called γs-set of G. Let D be a minimum secure dominating set in G. The secure dominating set S⊆ V(G)\D is called an inverse secure dominating set with respect to D. The inverse secure domination number of G denoted by γs−1(G) is the minimum cardinality of an inverse secure dominating set in G. An inverse secure dominating set of cardinality γs−1(G) is called γs−1-set. A disjoint secure dominating set in G is the set C = D ∪ S ⊆ V(G). The disjoint secure domination number of G denoted by γγr(G) is the minimum cardinality of a disjoint secure dominating set in G. A disjoint secure dominating set of cardinality γγs(G) is called γγs-set. In this paper, we show that every integers k and n with k ∈ {2, 4, 5, ...n − 1, n} is realizable as disjoint secure domination number, and order of G respectively. Further, we give the characterization of the disjoint secure dominating set in the join of two graphs.

Secure Skyline Queries on Cloud Platform.

Outsourcing data and computation to cloud server provides a cost-effective way to support large scale data storage and query processing. However, due to security and privacy concerns, sensitive data (e.g., medical records) need to be protected from the cloud server and other unauthorized users. One approach is to outsource encrypted data to the cloud server and have the cloud server perform query processing on the encrypted data only. It remains a challenging task to support various queries over encrypted data in a secure and efficient way such that the cloud server does not gain any knowledge about the data, query, and query result. In this paper, we study the problem of secure skyline queries over encrypted data. The skyline query is particularly important for multi-criteria decision making but also presents significant challenges due to its complex computations. We propose a fully secure skyline query protocol on data encrypted using semantically-secure encryption. As a key subroutine, we present a new secure dominance protocol, which can be also used as a building block for other queries. Finally, we provide both serial and parallelized implementations and empirically study the protocols in terms of efficiency and scalability under different parameter settings, verifying the feasibility of our proposed solutions.

Connected minimum secure-dominating sets in grids

For any (finite simple) graph G the secure domination number of G satisfies γs(G)≥|V(G)|2. Here we find a secure-dominating set S in G such that |S|=⌈|V(G)|2⌉ in all cases when G is a grid, and in the majority of cases when G is a cylindrical or toroidal grid. In all such cases, S satisfies the additional requirement that G[S] is connected. We make note that the concept of secure-dominating sets considered in this paper is quite different from the other secure domination currently of interest.11The other sort of secure domination: A dominating set S⊆V(G) is secure dominating (in G) if and only if for every v∈V(G)∖S there is some u∈S such that (S∖{u})∪{v} is dominating, in G.

On secure domination in trees

A subset D of the vertex set of a graph G is a secure dominating set of G if D is a dominating set of G and if, for each vertex u not in D, there is a vertex v in D adjacent to u such that the swap set (D \\ {v}) ∪ {u} is again a dominating set of G. The secure domination number of G, denoted by γs(G), is the cardinality of a smallest secure dominating set of G. In this paper, we prove that for any tree T on n ≥ 3 vertices, and the bounds are sharp, where ℓ and t are the numbers of leaves and stems of T , respectively. Moreover, we characterize the trees T such that .

A characterization of trees with equal independent domination and secure domination numbers

Let i(G) and γs(G) be the independent domination number and secure domination number of a graph G, respectively. Merouane and Chellali (2015) [12] proved that i(T)≤γs(T) for any tree T and asked to characterize the trees T with i(T)=γs(T). In this paper, we answer the question. We introduce three operations on trees and prove that any tree T with i(T)=γs(T) can be obtained by these operations.

Upper Secure Domination Number of a Graph

A subset S of V is a dominating set of a graph G=(V,E) if every vertex in V\\S is adjacent to a vertex in S. A dominating set S is called a secure dominating set if for each v∈V\\S there exists u∈S such that v is adjacent to u and S1=(S−{u})∪{v} is a dominating set. The maximum cardinality of a minimal secure dominating set of G is called the upper secure domination number of G and is denoted by Γs(G). In this paper we initiate a study of this parameter and present several basic results.

Further results on secure restrained domination in graphs

Let G=(V, E) be a graph and let S ⊆ V. The set S is a dominating set of G if every vertex in V \\ S is adjacent to some vertex in S. The set S is a restrained dominating set if every vertex in V \\ S is adjacent to a vertex in S and to a vertex in V \\ S. The minimum cardinality of a restrained dominating set is called restrained domination number of G and it is denoted by γr(G). A set S ⊆ V(G) is called a secure (restrained) dominating set if S is (restrained) dominating and for all u ϵ V \\ S there exists v ϵ S ∩ N(u) such that (S \\ {v}) ∪ {u} is (restrained) dominating. The minimum cardinality of a secure (restrained) dominating set is a secure (restrained) domination number of G and it is denoted by γs(G) (γsr(G)). In this paper we characterize few classes of graphs for which γr(G)=γsr(G) and γs(G)=γsr(G). Specific values of certain graphs are determined and Nordhaus Gaddum type results are discussed.

Edge criticality in secure graph domination

A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set X−{v}∪{u} is again a dominating set of G. The secure domination number of G is the cardinality of a smallest secure dominating set of G. A graph G is q-critical if the smallest arbitrary subset of edges whose removal from G necessarily increases the secure domination number, has cardinality q. In this paper we characterise q-critical graphs for all admissible values of q and determine the exact values of q for which members of various infinite classes of graphs are q-critical.

On minimum secure dominating sets of graphs

A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X/{v}) ᑌ {u} is again a dominating set of G, in which case v is called a defender. The secure domination number of G is the cardinality of a smallest secure dominating set of G. In this paper, we show that every graph of minimum degree at least 2 possesses a minimum secure dominating set in which all vertices are defenders. We also characterise the classes of graphs that have secure domination numbers 1, 2 and 3.