Abstract
The resistance distance between any two vertices of a connected graph G is defined as the effective resistance between them in the electrical network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index is a resistance distance-based topological index which plays an essential role in the study of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). In this paper, using techniques from electric network theory and graph theory, we characterize pentagonal chains with extermal Kirchhoff indices.
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