SUPER PAIR SUM LABELLING OF GRAPHS
SUPER PAIR SUM LABELLING OF GRAPHS THEOREM:4.1 Any path is a super pair sum graph. Proof: Let u_1,u_2,…..,u_nbe the vertices of the path p_n. Case(i) n is odd. Define f:V(G)∪E(G)→{0,±1,±2,….,±(n-1) as follows: f(u_i )= {█((i+1-2n)/2 if i is odd@(n+i-1)/2 if i is even )┤ and f(u_i u_(i+1) )= (2i-n+1)/2,1≤i≤n-1 thus, f is a super pair sum labelling. Case(ii). n is even Define f:V(G)∪E(G)→{0,±1,±2,….,±(n-1) as follows: f(u_i )={█(((3n+2i-4)/2 , (1≤i≤n/2 ,i is odd and n≡2(mod4))¦(2≤i≤n/2, i is even and n≡0(mod4) ))¦((n+2i-4)/4, ((n+4)/2≤i≤n-1,i is odd and n≡2(mod4))¦((n+4)/2≤i≤n,i is even n≡0(mod4) ))@((2-3n+2i)/4 , (2≤i≤(n-2)/2,i is even and n≡2(mod4))¦(1≤i≤(n-2)/2 ,i is odd andn≡0(mod4)))¦((2-5...