Infinite family of 2-connected transmission irregular graphs

Andrey A. Dobrynin

Applied Mathematics and Computation, 2019, vol. 340, issue C, 1-4

Abstract: Distance between two vertices is the number of edges in the shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

Keywords: Vertex transmission; Transmission irregular graph; Wiener complexity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:1-4

DOI: 10.1016/j.amc.2018.08.042

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