We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price o...

In behavioral experiments the respondents make their choices based on several factors called attributes. When the attributes are related to benefits and costs and respondents choose one attribute at a time, the highest level for benefit attributes and the lowest level for cost attributes will be selected. The relative importance given by the respondents to the attributes is not determined. If a...

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

Multi-objective optimisation yields an estimated Pareto front of mutually non- dominating solutions, but with more than three objectives, understanding the relationships between solutions is challenging. Natural solutions to use as landmarks are those lying near to the edges of the mutually non-dominating set. We propose four definitions of edge points for many-objective mutually non-dominating...

Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination prob...

In a graph G, a vertex dominates itself and its neighbors. A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. The minimum cardinality taken over all, the minimal double dominating set which is called Fuzzy Double Domination Number and which is denoted as ) (G fdd  . A set V S  is called a Triple dominating set of a graph G if every ...

Abstract This article introduces a type of dominating property, partially inherited from L. Chen’s, and proves an existence uniqueness theorem concerning common best proximity points. A certain kind boundary value problem involving the so-called Caputo derivative can be formulated so that our result applies.