<p>Dutch windmill graph [1, 2] and denoted by <em>Dnm</em>. Order and size of Dutch windmill graph are (<em>n</em>−1)<em>m</em>+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, <em>M</em>-polynomials and some topological indices in term of the <em>M</em>-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.</p>

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., ℛ D D Z = 1 / 2 ∑ μ , ν ∈ V Z ( d Z μ + d Z ν / d Z μ , ν ) . Eliasi and Taeri proposed four new graphic unary operations: S Z , ℛ Z , Q Z , and T Z , frequently implemented in sum of graphs, symbolized as Z 1 + Z 2 ℱ , i.e., sum of two graphs ℱ Z 1 , Z 2 ; 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.