Graceful Chromatic Numbers of Three Variants of Triangular Ladder Graphs
DOI:
https://doi.org/10.53696/venn.v5i5.682Keywords:
Graceful Chromatic Number, Graceful Coloring, Triangular Ladder Graphs, Bridge Triangular Ladder Graphs, Circular Triangular Ladder GraphAbstract
A graceful k-coloring of a graph G is a proper vertex coloring f: V(G) → {1, 2, ..., k}, where k ≥ 2, which induces a proper edge coloring f*: E(G) → {1, 2, ..., k − 1}, defined by f*(uv) = |f(u) − f(v)| for every edge uv ∈ E(G). The graceful chromatic number of G, denoted by chi_g(G), is the minimum integer k for which G admits a graceful k-coloring. This study determines the graceful chromatic numbers of the variation triangular ladder graph, the bridge triangular ladder graph, and the circular triangular ladder graph.
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