A structural approach to the graceful coloring of a subclass of trees
D. Laavanya, Devi Yamini S · Heliyon · 2023
Let M = \{ 1 , 2 , . . m \} and G be a simple graph. A graceful m -coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M ∖ \{ m \} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number χ g \( G \) = min \{ m : G admits a gracefulm− coloring \} . We prove that 5 ≤ χ g \( T \) ≤ 7 , where T is a tree with Δ = 4 . Furthermore, we categorize the trees into three types along with its characterization and the related coloring algorithm are presented in this study.