In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . T...Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . The cardinality of a minimum resolving set is called the resolving number or dimension of and is denoted by . A resolving set is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path. The minimum cardinality of these sets, denoted respectively by and are called the star resolving number and path resolving number. In this paper we investigate these re-solving parameters for the hypercube networks.展开更多
An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinali...An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinality of a resolving set of G. A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.展开更多
文摘In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
文摘Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . The cardinality of a minimum resolving set is called the resolving number or dimension of and is denoted by . A resolving set is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path. The minimum cardinality of these sets, denoted respectively by and are called the star resolving number and path resolving number. In this paper we investigate these re-solving parameters for the hypercube networks.
文摘An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinality of a resolving set of G. A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.
