HARMONIC DEGREE-BASED INDEX OF SPECIAL CHEMICAL MOLECULAR AND NANOTUBES

Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. Suppose G is a connected molecular graph and vertices u,v epsilon V(G). In this paper, we present explicit formulas for calculating the "general harmonic index, harmonic index and Harmonic polynomial" of a special chemical molecular graph "Cas(C)-CaR(C)[m,n,p] Nanotubes Junction" are given. The Cas(C)-CaR(C)[m,n,p] Nanotubes Junction is a new nano-structure that was defined by M.V. Diudea, on based the new graph operations (Leapfrog Le and Capra Ca) on the cycle graph C-n. In this paper, we compute the harmonic index vie two ways namely degree-based method and via polynomial method.