… The minimum cardinality of a connected resolving set in a graph G is its connected …
graph Kn and the star K1,n−1 are the only connected graphs of order n ⩾ 3 having connected …

… If we are given a minimum resolving partition Π of a connected graph G, then we can find a
connected resolving partition Π of G, where Π is a refinement of Π. Indeed, the partition each …

… graphs are established. It is shown that dim(H)⩽dim(H×K 2 )⩽dim(H)+1 for every connected
graph H… ε, there exists a connected graph G and a connected induced subgraph H of G such …

… connected resolving set W in a graph G is the connected resolving number cr{G). A connected
… The minimum cardinality of a connected resolving set W in a graph G is the connected …

… finding the minimum connected resolving set of graphs. A vertex set B of a connected graph
G resolves … A resolving set B of G is connected if the subgraph B induced by B is a nontrivial …

… Also, we ignore the direct product of two bipartite graphs, which is not connected, and
therefore, not interesting for our purposes. In this section we mainly deal with the case in which at …

… We also study the partition dimension of a family of circulant graphs Xn,4 with connection set
C = {… We also consider a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and …

… However, the complete graph K, is not the only connected graph of order n with resolving
number n - 1 as we have seen in Proposition 2.1(c). By Theorem A(d) and (l), we are able to …

… A vertex v of a connected graph G is said to distinguish two vertices x and y of G if dG (v, x)=
dG (v, y), ie, the distance between v and x is different from the distance between v and y. A …

… A strong metric basis of a connected graph G is a subset S ⊆ V of its vertices, such that for
… partitioning of the vertex set and resolvability. Let G be a connected graph, For a subset S of …