Huihui Zhang ; Jing Chen ; Shuchao Li - The quotients between the (revised) Szeged index and Wiener index of graphs

dmtcs:1514 - Discrete Mathematics & Theoretical Computer Science, May 9, 2017, Vol. 19 no. 1 - https://doi.org/10.23638/DMTCS-19-1-12
The quotients between the (revised) Szeged index and Wiener index of graphsArticle

Authors: Huihui Zhang ; Jing Chen ; Shuchao Li

    Let $Sz(G),Sz^*(G)$ and $W(G)$ be the Szeged index, revised Szeged index and Wiener index of a graph $G.$ In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order $n\geqslant 10$ are characterized; as well the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results, further relation on the quotients between the (revised) Szeged index and the Wiener index are studied. Sharp lower bound on $Sz(G)/W(G)$ is determined for all connected graphs each of which contains at least one non-complete block. As well the connected graph with the second smallest value on $Sz^*(G)/W(G)$ is identified for $G$ containing at least one cycle.


    Volume: Vol. 19 no. 1
    Section: Graph Theory
    Published on: May 9, 2017
    Accepted on: April 14, 2017
    Submitted on: May 8, 2017
    Keywords: Mathematics - Combinatorics,05C69, 05C05

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