Puzzling and apuzzling graphs
Daphne Gold, James M. Henle, Cherry Huang, Tia Lyve, Tara Marin, Jasmine Osorio, Mäneka Puligandla, Bayla Weick, Jing Xia, Yun He, Jize Zhang · AKCE International Journal of Graphs and Combinatorics · 2016
Let be a graph with chromatic number and consider a partition of into connected subgraphs. is a puzzle on if there is a unique vertex coloring of using 1, 2, …, such that the sums of the numbers assigned to the partition pieces are all the same. is an apuzzle if there is a unique vertex coloring such that the sums are all different.We investigate the concept of puzzling and apuzzling graphs, detailing classes of graphs that are puzzling, apuzzling and neither.