**About the Editor**

**Ismael Gonz ´alez Yero** is an Associate Professor of Applied Mathematics at the University of Cadiz, Spain. He earned his Ph.D. in Mathematics (2010) from Rovira I Virgili University, Spain. His research work focuses on graph theory, specifically on parameters related to distances and domination in graphs, metric graph theory and products of graphs, and their applications in computer science, with some emphasis on privacy in social networks and community detection. He is the author of about 100 research papers on these topics.

### **Preface to "Distances and Domination in Graphs"**

In graph theory, a large number of topics related to distances in graphs is being investigated in several studies. The most typical and known ones are perhaps the diameter, the radius, and the eccentricity. However, there is a large number of other interesting distance-related topcis in graphs that are frequently used in applied and/or theoretical investigations. Some of the most common ones are related to well-known indexes that measure the properties of graphs, for example, the centrality, the closeness, and the betweenness centrality. One interesting fact that allows us to deal with such problems is that the matrix of distances in a graph can be computed in polynomial time, using, for example, the well-known Floyd–Warshall algorithm. Another interesting case in problems concerning distances in graphs is the degree–diameter problem, which basically involves the determination of the largest possible graph (in terms of the size of its vertex set) such that the largest degree of any of the vertices in the graph is, at most, the specified diameter. This problem has been extensively studied, and there is a huge background of literature on it. Some other examples of distance-related parameters are the convexity number, the geodetic number, and the metric dimension. During the last 30 years, with the increase in investigations in several areas like computer science, computer engineering, operational research and social networks, graph theory has become an important tool for researching many of the mentioned areas. On the other hand, one of the most important topics in graph theory is the theory of domination and related problems, such as independence, covering and matching. The growth of studies on domination in graphs can be partly attributed to its applicability in diverse theoretical fields, such as linear algebra, communication networks, social sciences, computational complexity and algorithm design. The significant increase in interest in this topic has resulted in an enormous quantity of published papers—around 1600 papers, a significant number of monographs and theses, and several books. Based on this increased interest, this Special Issue was developed at the journal *Mathematics* under the title of "Distance and Domination in Graphs", in order to gather some relavant and recent investigations concerning distances and domination in graphs.

> **Ismael Gonz´alez Yero** *Editor*
