G-Designs for Tadpole Graphs
Cole Jacobs · University of Minnesota Digital Conservancy (University of Minnesota) · 2025
We investigate the existence of G-designs for the tadpole family of graphs. Specifically, we show that for any tadpole graph G on n edges, G decomposes the complete graph on 2nk edges, and 2nk+1 edges, for any positive integer k. These tadpole graphs are classified into two cases: Those with an odd cycle, and those with an even cycle. For each case, graph labeling algorithms are defined for both rho-tripartite labelings and 1-rotational rho-tripartite labelings.