ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS

ON SOME FAMILIES OF LINEAR DIOPHANTINE GRAPHS

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

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Abstract

Linear 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 Linear Diophantine labeling or not, and if yes, we will find such a Linear 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 Linear Diophantine nature. We refer to a Linear Diophantine Graph as an LDG.

Keywords

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