Affordable Access

Weak total resolving sets in graphs

Authors
  • Javaid, Imran
  • Salman, Muhammad
  • Murtaza, Mahr
  • Iftikhar, Farheen
  • Imran, Muhammad
Type
Preprint
Publication Date
Aug 04, 2014
Submission Date
Aug 04, 2014
Identifiers
arXiv ID: 1408.0649
Source
arXiv
License
Yellow
External links

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 $w\in W$, there is at least one element in $W-\{w\}$ that resolves $w$ and $v$ for every $v\in V(G)- W$. 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 $k$-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.

Report this publication

Statistics

Seen <100 times