Graceful Chromatic Numbers of Three Variants of Triangular Ladder Graphs

Raphita Yanisari Silalahi (Universitas Pendidikan Ganesha)
I Nengah Suparta (Universitas Pendidikan Ganesha)
Sariyasa Sariyasa (Universitas Pendidikan Ganesha)
Rasmin Siringo-ringo (Universitas Pendidikan Ganesha)
Kadek Ria Andriani (Universitas Pendidikan Ganesha)

Venn: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences
Vol. 5 No. 5 (2026): Volume 5 Nomor 5 Tahun 2026

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.