Unveiling New Cube Sum Graphs
Milankumar K. Kansagara, Gaurang V. Ghodasara · Indian Journal of Industrial and Applied Mathematics · 2025
Let G = (V, E) be a (p, q) graph, where p is the order and q is the size of G. An injective function f : V (G) -? {1, 2, . . ., p is said to be a cube sum labeling if the induced each labeling function f* (uv) = f (u)3 + f (v)3 is injective. A graph admitting a cube sum labeling is called a cube sum graph. In this study, an investigation is conducted in to that the ladder graph Ln, the tadpole graph T (m, n), the cycle with triangle Cn(1, 1, n - 2), the k-polygonal snake graph Sn(Ck) for odd k and the one point union Ck(n) as cube sum graph. These results involve determining whether the Diophantine equation a3 + b3 = c3 + d3 has an integer solution or not.