For an ordered subset W= w 1, w 2,… wk of vertices and a vertex u in a connected graph G,
the representation of u with respect to W is the ordered k-tuple r (u| W)=(d (u, w 1), d (u, w …

The number of edges in a shortest walk (without repetition of vertices) from one vertex to
another vertex of a connected graph G is known as the distance between them. For a vertex …

For an ordered set W={w_1, w_2,..., w_k} of vertices and a vertex v in a connected graph G,
the representation of v with respect to W is the ordered k-tuple r (v| W)=(d (v, w_1), d (v …

The problem of uniquely recognizing the position of an intruder in a network was the
principal motivation of introducing the concept of metric generators in graphs by Slater in …

Coronoid systems are actually geometric arrangements of six-sided benzenoids in
hexagonal form. Coronoid systems are organic chemical structures, that fall into two …

A shortest path between two vertices u and v in a connected graph G is au− v geodesic. A
vertex w of G performs the geodesic identification for the vertices in a pair (u, v) if either v …

Let r=(V, E) be a simple connected graph having V and E as the vertex-and edge-sets,
respectively. A set H⊆ V is said to be a dominating set in graph r if for every u∈ V− H there …

Research Article Classes of Planar Graphs with Constant Edge Metric Dimension Page 1
Research Article Classes of Planar Graphs with Constant Edge Metric Dimension Changcheng …

A vertex v of a connected graph G identifies a pair (x, y) of vertices if the number of edges in
av− x geodesic (shortest path) is different from the number of edges in v− y geodesic. A …

A shortest path between two vertices u and v in a connected graph G is au− v geodesic. A
vertex w of G performs the geodesic identification for the vertices in a pair (u, v) if either v …