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Alliances and related parameters in graphs
Henning Fernau, Juan A. Rodriguez-Velazquez
In this paper, we show that several graph parameters are known in different areas under completely different names. More specifically, our observations connect signed domination, m…
On the (adjacency) metric dimension of corona and strong product graphs and their local variants: combinatorial and computational results
Juan A. Rodríguez-Velázquez, Henning Fernau
The metric dimension is quite a well-studied graph parameter. Recently, the adjacency metric dimension and the local metric dimension have been introduced. We combine these variant…
The Hosoya polynomial of distance-regular graphs
Emeric Deutsch, Juan A. Rodriguez-Velazquez
In this note we obtain an explicit formula for the Hosoya polynomial of any distance-regular graph in terms of its intersection array. As a consequence, we obtain a very simple for…
Strong metric dimension of rooted product graphs
Dorota Kuziak, Ismael G. Yero, Juan A. Rodríguez-Velázquez
Let be a connected graph. A vertex strongly resolves a pair , of vertices of if there exists some shortest path containing or some shortest path…
Computing the metric dimension of a graph from primary subgraphs
D. Kuziak, J. A. Rodríguez-Velázquez, I. G. Yero
Let be a connected graph. Given an ordered set and a vertex , the representation of with respect to is the ordered…
On the local metric dimension of corona product graphs
Juan A. Rodriguez-Velazquez, Gabriel A. Barragan-Ramirez, Carlos Garcia Gomez
A vertex is said to distinguish two vertices of a nontrivial connected graph if the distance from to is different from the distance from t…