## Abstract

A set W of vertices of G is said to be a weak total resolving set for G if W is a resolving set for G as well as for each w G W and for each v V(G)-W> there is one element in W-{u>} that resolves w and v. Weak total metric dimension of G is the smallest order of a weak total resolving set for G. This paper includes the investigation of weak total metric dimension of trees. Also, weak total resolving number of a graph as well as randomly weak total fc-dimensional graphs are defined and studied in this paper. Moreover, some characterizations and realizations regarding weak total resolving number and weak total metric dimension are given.

Original language | English |
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Pages (from-to) | 11-26 |

Number of pages | 16 |

Journal | Utilitas Mathematica |

Volume | 110 |

Publication status | Published - Mar 2019 |

## Keywords

- Metric dimension
- Randomly weak total k-dimensional graph
- Twins
- Weak total metric dimension
- Weak total resolving number

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics