A vertex u in a graph G resolves a pair of distinct vertices x, y of G if the distance between u and x is different from the distance between u and y. A set W of vertices in G resolves the graph G if every pair of distinct vertices of G is resolved by some vertices in W . The metric dimension of a graph, denoted by dim(G), is the smallest cardinality of a resolving set. A resolving set W for a ...

A set S of vertices in a graph G is a resolving set if for every pair of vertices u, v ∈ V (G) there is a vertex x ∈ S such that the distances d(x, v) 6= d(x, u). We define a new parameter res(G), the size of the smallest subset S of V (G) that is not a resolving set but every superset of S resolves G. We also demonstrate that for every triple (a, b, c), a ≤ (b + 1) ≤ c, there is a graph G in w...

This paper presents an algebra for conflict resolution in nonlinear planning. A set of conflicts in a plan is considered as a constraint network. Each node in the network represents a conflict, and is associated with a set of alternative ways for resolving it. Thus, resolving conflicts in a plan corresponds to selecting a set of consistent resolution methods so that, after they are applied to t...

For a simple connected graph G=(V,E), an ordered set W⊆V, is called resolving of G if for every pair two distinct vertices u and v, there element w in W such that d(u,w)≠d(v,w). A metric basis with minimum cardinality. The dimension the cardinality it denoted by β(G). In this article, we determine power finite paths characterize all bases same.

For an ordered set { } k w w w W , , , 2 1  = of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), ..., d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G ...

Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by modeling it as the minimum weighted doubly resolving set (DRS) problem, which is a strengthening of the well-known metric dimension problem. Let G be a vertex weigh...

Medical treatment decision making is a good application of knowledge representation and reasoning. We are particularly interested in using them to resolve treatment conflicts, a complicated condition when two treatments cannot be given simultaneously to a patient suffering from multiple symptoms. The logic system is required to reason on cases with and without treatment conflicts. Thanks to the...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U . A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W . Determining (resolving) sets are said to have the exchange property in G if whenever S and R are minimal determining (resolvi...

Federated databases are one of the challenges for database system builders. In an e ort to create these systems, current implementations require every member of the federation to agree to a particular standard. We examine query optimization under the Z39.50 standard for heterogeneous library information systems, looking speci cally at the problem of managing temporary relations within a library...