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On 2-Connected Transmission Irregular Graphs

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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 problemwas 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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. A. Dobrynin

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  1. A. A. Dobrynin
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Correspondence to A. A. Dobrynin.

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Original Russian Text © A.A. Dobrynin, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 4, pp. 5–14.

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Dobrynin, A.A. On 2-Connected Transmission Irregular Graphs. J. Appl. Ind. Math. 12, 642–647 (2018). https://doi.org/10.1134/S199047891804004X

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  • DOI: https://doi.org/10.1134/S199047891804004X

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