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- Title
Extremal Phenylene Chains with Respect to the Kirchhoff Index and Degree-based Topological Indices.
- Authors
Yujun Yang; Dayong Wang
- Abstract
The resistance distance between any two vertices of a graph G is defined as the net effective resistance between them in the network construct from G by replacing each edge of G with a unit resistor. The Kirchhoff index of G is defined as the sum of resistance distances between all pairs of vertices. Let Ln (resp. Hn) be the linear phenylene chain (resp. helicene phenylene chain) containing n hexagons and n-1 squares. In this paper, firstly, it is shown that among all phenylene chains with n hexagons and n-1 squares, Ln attains the maximum value of the Kirchhoff index. Moreover, it is demonstrated that the minimum Kirchhoff index is attained only when the phenylene chain is an "all-kink" chain, which leads to the conjecture that Hn has the minimum Kirchhoff index. Secondly, exact expressions for some degree-based topological indices, namely, the general Randić index, the Harmonic index, the first Zagreb index, the Sum-Connnectivity index, the Geometric-Arirthmetic index, the Atom-Bond connectivity index, and the Symmetric-Division index of phenylene chains are obtained, with extremal phenylene chains with respect to these degreebased topological indices being characterized.
- Subjects
ZAGREB (Croatia); TOPOLOGICAL degree; MOLECULAR connectivity index; RESPECT; HEXAGONS
- Publication
IAENG International Journal of Applied Mathematics, 2019, Vol 49, Issue 3, p274
- ISSN
1992-9978
- Publication type
Article