Abstract
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.
Highlights
A query at a vertex v discovers or verifies all edges and non-edges whose endpoints have different distance from v
A resolving set W is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path
In the network verification problem [1], the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges
Summary
A query at a vertex v discovers or verifies all edges and non-edges whose endpoints have different distance from v. In the network verification problem [1], the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph [2]. A graph-theoretic interpretation of this problem is to provide representations for the vertices of a graph in such a way that distinct vertices have distinct representations. Solving set for G is called the resolving number or dimension and is denoted by dim G
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
