Trees with Given Number of Pendant Edges and Their Wiener Indices

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Advances and Applications in Mathematical Sciences




The Wiener index (the sum of the distances between all pairs of vertices) is one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. Extremal trees that maximize or minimize the Wiener index among different categories of trees are extensively studied and identified in previous work. While the structure with given number of pendant edges are of interest in quantum chemistry, we provide a short review on this topic. We use the previously obtained results to characterize trees (chemical trees) that achieve the maximum and minimum Wiener index, given the number of vertices and the number of pendant edges. As a consequence, simple calculation will give upper and lower bounds of the Wiener index of these trees.