ON LEGENDRE ABSOLUTE DIFFERENCE CORDIAL LABELING OF SOME SPECIAL GRAPHS

R. Anusuya, G. Priscilla Pacifica

Abstract: Cahit originally proposed the premise of cordial labelling in 1987. Legendre Cordial Labelling initially emerged by Jason D. Andoyo & F. Rulete in 2025. Inspired by this effort, we designed Legendre Absolute Difference Cordial Labelling. A bijection ϱ:V(G)→1,2,..,V is typically referred to as a Legendre absolute difference cordial labelling modulo ρ , wherein ρ constitutes an odd prime, assuming G as basic connected graph while the resultant map ϱρ*:EG→{0,1} laid out as ϱρ*μν=0 if δμνρ=-1 or δμν=0 , & ϱρ*μν=1 if δμνρ=1 or δμν=1 , whence ϱμ-ϱ(ν)≡δμν (mod ρ) , 0≤δμν<ρ , fulfills the condition |eϱρ*0-eϱρ*1|≤1, whence eϱρ*i remains the count of labelled edges i (i=0,1) . The analysis of Legendre absolute difference cordial labelling modulo ρ for certain networks, such as Y-tree graph, F- tree graph, Triangular snake graph and Trianglar book graph.