On Transmission Irregular Cubic Graphs of an Arbitrary Order

The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions. In 2018, Alizadeh and Klavžar posed the following question: do there exist infinite families of regular TI graphs? An infinite family of TI cubic graphs of order 118+72k, k≥0, was constructed by Dobrynin in 2019. In this paper, we study the problem of finding TI cubic graphs for an arbitrary number of vertices. It is shown that there exists a TI cubic graph of an arbitrary even order n≥22. Almost all constructed graphs are contained in twelve infinite families

On Transmission Irregular Cubic Graphs of an Arbitrary Order

The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions. In 2018, Alizadeh and Klavžar posed the following question: do there exist infinite families of regular TI graphs? An infinite family of TI cubic graphs of order 118+72k, k≥0, was constructed by Dobrynin in 2019. In this paper, we study the problem of finding TI cubic graphs for an arbitrary number of vertices. It is shown that there exists a TI cubic graph of an arbitrary even order n≥22. Almost all constructed graphs are contained in twelve infinite families

Individual inter-annual nest-site relocation behaviour drives dynamics of a recently established Barnacle Goose Branta leucopsis colony in sub-arctic Russia

Avian breeding colonies are generally in a continuous state of flux, some parts growing whilst others shrink as individuals move within the colony on the search for better nest-sites. We examined the role of experience in breeding patch choice by individually marked Barnacle Geese Branta leucopsis in a recently established colony in sub-arctic Russia. Individuals failing to reproduce successfully tended to shift nest location further the following season than did successful pairs, and they did so towards the most dense nest aggregations within the colony, where reproductive success was higher. We suggest that individual decisions on nest-site choice shape the spatial dynamics of this colony