ON SOME FAMILIES OF DIOPHANTINE GRAPHS

ON SOME FAMILIES OF DIOPHANTINE GRAPHS

O. M. Salama, M.A. Seoud, M. Anwar, A. Elsonbaty

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Abstract

Diophantine labeling of graphs is an extension of the prime labeling of graphs. In this manuscript, we introduce some necessary conditions for determining whether a given graph admits Diophantine labeling or not, and if yes, we will find such a Diophantine labeling. We also study specific families of graphs, including the Complete graphs Kn, Wheel graphs Wn and Wn,n, Circulant graphs Cn(j), Path graphs Pn(j), Cartesian product graphs C3 × Cm, Normal Product graphs Pn ◦ Pn, Corona graphs G ⊙H, Double Fan graphs gn = Pn +K2, Power graphs P2 n and P3 n, to ascertain their Diophantine nature.

Keywords

Graph labeling, Prime labeling, Diophantine labeling, Families of Diophantine graphs.