Weak total resolving sets in graphs

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.