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Sibirskii Zhurnal Industrial'noi Matematiki, 2009, Volume 12, Number 4, Pages 44–50 (Mi sjim581)  
This article is cited in 3 scientific papers (total in 3 papers)

The Wiener Index for Graphs of Arbitrary Girth and Their Edge Graphs

A. A. Dobrynin

Sobolev Institute of Mathematics, SB RAS, Novosibirsk
Full-text PDF (278 kB) Citations (3)
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Abstract: We consider the invariant $W(G)$ (Wiener index) of a simple connected nondirected graph $G$, which is equal to the sum of distances between all pairs of vertices in the natural metric. We show that for every $g\ge5$ there exist planar graphs $G$ with a shortest cycle of length $g$ for which $W(L(G))=W(G)$, where $L(G)$ is the edge graph for $G$.
Keywords: invariant graph, distance in graphs, Wiener index.
Received: 19.02.2009
English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 4, Pages 505–511
DOI: https://doi.org/10.1134/S1990478910040058
Bibliographic databases:
UDC: 519.17
Language: Russian
Citation: A. A. Dobrynin, “The Wiener Index for Graphs of Arbitrary Girth and Their Edge Graphs”, Sib. Zh. Ind. Mat., 12:4 (2009), 44–50; J. Appl. Industr. Math., 4:4 (2010), 505–511
Citation in format AMSBIB
\Bibitem{Dob09}
\by A.~A.~Dobrynin
\paper The Wiener Index for Graphs of Arbitrary Girth and Their Edge Graphs
\jour Sib. Zh. Ind. Mat.
\yr 2009
\vol 12
\issue 4
\pages 44--50
\mathnet{http://mi.mathnet.ru/sjim581}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2668810}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 4
\pages 505--511
\crossref{https://doi.org/10.1134/S1990478910040058}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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