Vertex Spans of Multilayered Cycle and Path Graphs

Abstract

In this paper, we observe a special class of graphs known as multilayered graphs and their subclasses, namely multilayered cycles and multilayered paths. These graphs model layouts of shopping malls, city street grids, and even resemble the topology of certain famous board games. We analyze the values of all vertex spans (strong, direct, and Cartesian span) for these subclasses of graphs. Surprisingly, our results for multilayered cycles reveal that, regardless of the chosen movement rules, the span values depend solely on the length of the individual cycles, rather than the number of layers. This finding carries significant implications for the application of graph spans in maintaining safety distances.