Orientations of hexagonal chains with extremal values of the Randić index. Issue 18 (27th May 2021)

• Record Type: Journal Article
• Authors: Bermudo, Sergio; Monsalve, Juan; Rada, Juan
• Is Part Of: International journal of quantum chemistry. Volume 121:Issue 18(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-05-27
• Subjects: extremal values -- hexagonal chain -- orientations -- Randić index; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.26744
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: Let D be a digraph with set of vertices V ( D ) and set of arcs A ( D ). Recently, the Randić index of D was extended to digraphs as 1 R D = 1 2 ∑ uv ∈ A D 1 d D + u d D − v, where d D + u and d D − v are the out‐degree and in‐degree of u and v, respectively. In this paper we study the extremal values of R over the set of all orientations of hexagonal chains with k hexagons. Abstract : Directed complex networks play an important role in biological networks, transportation networks, chemical and biochemical reactions in metabolic networks, or social networks, just to mention a few. Recently, the concept of vertex‐degree‐based topological indices of directed graphs was introduced, and in particular, the Randić index for directed graphs was studied. Among all orientations of hexagonal chains with a fixed number of hexagons, we show that the sink‐source orientation of the linear chain Lh attains the minimal value of the Randić index. On the other hand, among the orientations of hexagonal chains (with non‐adjacent angular hexagons), the maximal value of the Randi'c index is attained in the hexagonal chain F h .