The relation between different edge spans of a graph

Abstract

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. Mainly, vertex spans have been studied, in which players visit all the vertices of a graph. In this paper, we analyze the values of three edge spans, which represent the maximal safety distance that two players can maintain while visiting all the edges of a graph. We present edge span values for some graph classes and examine the relationship between different variants of edge spans.