Generalized Lucky Numbers for H(r) Architectures
Warakorn Bansiri, Ananya Anantayasethi, Kittisak Saengsura · Axioms · 2026
A lucky coloring of a graph G is an edge coloring induced by a vertex labeling, where each edge is assigned a color equal to the sum of the labels of its incident vertices, such that adjacent edges receive distinct colors. The lucky number of G, denoted by η(G), is the minimum integer k such that G admits a lucky coloring using labels from the set {1,2,3,…,k}. In this paper, we investigate the lucky numbers for the H(r) architectures, a sequence of r connected H-shaped structures. We establish the exact values for these graphs, proving that η(H(r))=6 for even r and η(H(r))=7 for odd r≥3.