Metric dimension and diameter in bipartite graphs | Zendy

Peter Dankelmann | Zendy; J.B. MORGAN | Zendy; Emily Rivett-Carnac | Zendy

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Metric dimension and diameter in bipartite graphs

Author(s) -

Peter Dankelmann,

J.B. MORGAN,

Emily Rivett-Carnac

Publication year - 2020

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2382

Subject(s) - mathematics , bipartite graph , metric dimension , combinatorics , dimension (graph theory) , metric (unit) , complete bipartite graph , discrete mathematics , graph , chordal graph , 1 planar graph , operations management , economics

Let G be a connected graph and W a set of vertices of G. If every vertex of G is determined by its distances to the vertices in W, then W is said to be a resolving set. The cardinality of a minimum resolving set is called the metric dimension of G. In this paper we determine the maximum number of vertices in a bipartite graph of given metric dimension and diameter. We also determine the minimum metric dimension of a bipartite graph of given maximum degree.

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