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Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 4, Pages 5–14 (Mi da905)  

On $2$-connected transmission irregular graphs

A. A. Dobrynin

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: The transmission of a vertex $v$ in a graph is the sum of the distances from $v$ to all other vertices of the graph. In a transmission irregular graph, the transmissions of all vertices are pairwise distinct. It is known that almost all graphs are not transmission irregular. Some infinite family of transmission irregular trees was constructed by Alizadeh and Klavžar [Appl. Math. Comput., 328, 113–118, 2018] and the following problem was formulated: Is there an infinite family of $2$-connected graphs with the property? In this article, we construct an infinite family of $2$-connected transmission irregular graphs. Tab. 2, illustr. 2, bibliogr. 21.

Keywords: graph, vertex transmission, transmission irregular graph, Wiener index.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00499
17-51-560008
The author was supported by the Russian Foundation for Basic Research (projects nos. 16-01-00499 and 17-51-560008).


DOI: https://doi.org/10.17377/daio.2018.25.620

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 642–647

Document Type: Article
UDC: 519.17
Received: 03.05.2018

Citation: A. A. Dobrynin, “On $2$-connected transmission irregular graphs”, Diskretn. Anal. Issled. Oper., 25:4 (2018), 5–14; J. Appl. Industr. Math., 12:4 (2018), 642–647

Citation in format AMSBIB
\Bibitem{Dob18}
\by A.~A.~Dobrynin
\paper On $2$-connected transmission irregular graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2018
\vol 25
\issue 4
\pages 5--14
\mathnet{http://mi.mathnet.ru/da905}
\crossref{https://doi.org/10.17377/daio.2018.25.620}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 4
\pages 642--647
\crossref{https://doi.org/10.1134/S199047891804004X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85057278731}


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