Weak total resolving sets in graphs

I. Javaid, M. Salman, M. Murtaza, F. Iftikhar, M. Imran

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)11-26
Number of pages16
JournalUtilitas Mathematica
Publication statusPublished - Mar 2019


  • 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


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