
doi: 10.2139/ssrn.4921345
Summary: We investigate the tight bounds of the locating rainbow vertex-connection number (RVCL) on the edge-comb product (ECP) of arbitrary pairs of graphs. Specifically, we present examples of graph pairs that attain the upper bound, as well as those that attain the lower bound. Furthermore, we identify graph pairs whose RVCL lies strictly between these two bounds. The RVCL is defined as the smallest positive integer such that a graph can be colored using rainbow vertex coloring (RVC), where the ordered partition of the resulting color classes is a resolving partition. To construct the locating rainbow coloring function, we employ a set-theoretic approach.
edge-comb product, Coloring of graphs and hypergraphs, rainbow-vertex path, rainbow code, partition dimension, twin sets, locating rainbow connection number, resolving partition
edge-comb product, Coloring of graphs and hypergraphs, rainbow-vertex path, rainbow code, partition dimension, twin sets, locating rainbow connection number, resolving partition
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