5 research outputs found
On the edge metric dimension of some classes of cacti
The cactus graph has many practical applications, particularly in radio communication systems. Let be a finite, undirected, and simple connected graph, then the edge metric dimension of is the minimum cardinality of the edge metric generator for (an ordered set of vertices that uniquely determines each pair of distinct edges in terms of distance vectors). Given an ordered set of vertices of a connected graph , for any edge , we referred to the -vector (ordered -tuple), as the edge metric representation of with respect to . In this regard, is an edge metric generator for if, and only if, for every pair of distinct edges implies . In this paper, we investigated another class of cacti different from the cacti studied in previous literature. We determined the edge metric dimension of the following cacti: and in terms of the number of cycles and the number of paths