Some More Results on Reciprocal Degree Distance Index and ℱ-Sum Graphs

Abstract

A chemical invariant of graphical structure Z is a unique value characteristic that remains unchanged under graph automorphisms. In the study of QSAR/QSPR, like many other chemical invariants, reciprocal degree distance has played a significant role to estimate the bioactivity of several compounds in chemistry. Reciprocal degree distance is a chemical invariant, which is the degree weighted version of Harary index, i.e., ℛDDZ=1/2∑μ,ν∈VZ(dZμ+dZν/dZμ,ν). Eliasi and Taeri proposed four new graphic unary operations: SZ,ℛZ,QZ, and TZ, frequently implemented in sum of graphs, symbolized as Z1+Z2ℱ, i.e., sum of two graphs ℱZ1, Z2;ℱ is one of the unary graphic operations S,ℛ,Q,T. This work provides constraints for the above-mentioned invariant for this binary graphic operation F-sum of graphs.