Extremal Problems for Topological Indices in Combinatorial Chemistry

Extremal Problems for Topological Indices in Combinatorial Chemistry

Topological indices of molecular graphs are related to several physicochemical characteristics; recently, the inverse problem for some of these indices has been studied, and it has some applications in the design of combinatorial libraries for drug discovery. It is thus very natural to study also extremal problems for these indices, i.e., finding graphs having minimal or maximal index. In this ...

The Inverse Problems for Some Topological Indices in Combinatorial Chemistry

In the original paper, Goldman et al. (2000) launched the study of the inverse problems in combinatorial chemistry, which is closely related to the design of combinatorial libraries for drug discovery. Following their ideas, we investigate four other topological indices, i.e., the sigma-index, the c-index, the Z-index, and the M(1)-index, with a special emphasis on the sigma-index. Like the Wie...

Extremal problems for degree-based topological indices

For a graph G, let σ(G) = ∑ uv∈E(G) 1 √ dG(u)+dG(v) ; this defines the sum-connectivity index σ(G). More generally, given a positive function t, the edge-weight t-index t(G) is given by t(G) = ∑ uv∈E(G) t(ω(uv)), where ω(uv) = dG(u) + dG(v). We consider extremal problems for the t-index over various families of graphs. The sum-connectivity index satisfies the conditions imposed on t in each ext...

Extremal Polyomino Chains of VDB Topological Indices

We show that the zig-zag chain Z3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {φij} under which the zig-zag chain Z3 n is an extremal value of the induced topological index T defined by T (G) = ∑ 1≤i≤j≤n−1 mijφij where G is a graph with n vertices and mij is the number of edges of...

Extremal Combinatorial Problems in Relational Data Base