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  • On Wiener index of graphs and their line graphs
    Cohen, Nathann ...
    The Wiener index of a graph ▫$G$▫, denoted by ▫$W(G)$▫, is the sum of distances between all pairs of vertices in ▫$G$▫. In this paper, we consider the relation between the Wiener index of a graph, ... ▫$G$▫, and its line graph, ▫$L(G)$▫. We show that if ▫$G$▫ is of minimum degree at least two, then ▫$W(G) \leq W(L(G))$▫. We prove that for every non-negative integer ▫$g_0$▫, there exists ▫$g>g_0$▫, such that there are infinitely many graphs ▫$G$▫ of girth ▫$g$▫, satisfying ▫$W(G) = W(L(G))$▫. This partially answers a question raised by Dobrynin and Mel'nikov and encourages us to conjecture that the answer to a stronger form of their question is affirmative.
    Source: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 64, no. 3, 2010, str. 683-698)
    Type of material - article, component part
    Publish date - 2010
    Language - english
    COBISS.SI-ID - 23929895

    Link(s):

    http://match.pmf.kg.ac.rs/electronic_versions/match64/n3/match64n3_683-698.pdf

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