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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 642–647
Volume 25, No 4, 2018, P. 5-14
UDC 519.17
A. A. Dobrynin
On 2-connected transmission irregular graphs
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 Klavzar [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.
DOI: 10.17377/daio.2018.25.620
Andrey A. Dobrynin 1
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: dobr@math.nsc.ru
Received 3 May 2018
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