Research On Puzzling Graphs

Abstract

In this paper, let χ (G) be the chromatic number of a graph G and Z be a partition of G into connected sub graphs. If Z is a puzzle on G then there exists a unique vertex coloring of G by 1, 2, …, χ(G) such that the sums of the numbers assigned to the partition pieces are all same. We investigate the concept of puzzling graphs on Ladder graph and Grid graphs.