Extremal values of vertex-degree-based topological indices over hexagonal systems with fixed number of vertices

Subtrees of spiro and polyphenyl hexagonal chains

“…Such indices include the subtree number (also called ρ-index in [13]), number of leaf-containing subtrees (also called "acceptable residue configurations" [14]), BC-subtree number [15], general vertex-degree-based indices [16][17][18], atom-bond connectivity [19][20][21][22], Merrifield-Simmons index (number of independent vertex subsets [13]), the Hosoya index (number of matchings [23,24]), the Kirchhoff index [25][26][27], the Zagreb index [28][29][30][31][32], the Randić index [33][34][35][36], the Szeged index [11,37,38], and the PI index [39,40]. As one of the main structure-based and counting-based indices, the number of subtrees is known to be "negatively correlated" with the Wiener index [41].…”

The linear chain as an extremal value of VDB topological indices of polyomino chains

“…(2) As we can see, the Randić index, the sum-connectivity index, the harmonic index and the geometric-arithmetic index satisfy the conditions in part 1 of Theorem 2.6, while the first Zagreb index and the second Zagreb index satisfy conditions in part 2 of Theorem 2.6. We note that we cannot apply Theorem 2.6 on the atom-bond-connectivity index and the augmented Zagreb index since (2) (3) In fact, the unique polyomino chain with three squares different from the linear chain has atom-bond-connectivity index smaller than the linear chain. Similarly occurs with the augmented Zagreb index.…”

“…i+j [27], the geometricarithmetic index from ϕ ij = 2 √ ij i+j [23], the first Zagreb index from ϕ ij = i + j and the second Zagreb index from ϕ ij = ij [8], the atom-bond-connectivity index from ϕ ij = i+j−2 ij [6] and the augmented Zagreb index from ϕ ij = ij i+j−2 3 [7]. For recent publications on VDB topological indices we refer to ( [2], [4], [9], [10], [19], [20]).…”

Lower bounds for the number of inlets of hexagonal systems

“…In fact, Harary and Harborth [12] showed that 1 [12] Using Upper bounds for the number of inlets r over Λ n and Γ m were studied in refs. [13,14], where applications to VDB topological indices were…”