Edge spans and the minimal number of steps for keeping the safety distance

In several recent papers, the maximal safety distance that two players can maintain while moving through a graph has been defined and studied using three different spans of the graph, each with different movement conditions. In this paper, we analyze the values of these three edge spans, which represent the maximal safety distance that two players can maintain while visiting all the edges of the graph. We present results for various graph classes and examine the relationship between edge spans and vertex spans. Additionally, we provide some findings on the minimal number of steps required for walks through a graph to visit all the vertices or edges while maintaining the maximal safety distance.