A new upper bound for the total vertex irregularity strength of graphs |
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| Authors: | Marcin Anholcer Maciej Kalkowski Jakub Przyby&#x;o |
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| Institution: | aPoznań University of Economics, Al. Niepodległ ości 10, 60-967 Poznań, Poland;bAdam Mickiewicz University, ul. Wieniawskiego 1, 61-712 Poznań, Poland;cAGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland |
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| Abstract: | We investigate the following modification of the well-known irregularity strength of graphs. Given a total weighting w of a graph G=(V,E) with elements of a set {1,2,…,s}, denote wtG(v)=∑e vw(e)+w(v) for each v V. The smallest s for which exists such a weighting with wtG(u)≠wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of this graph, and is denoted by  . We prove that  for each graph of order n and with minimum degree δ>0. |
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| Keywords: | Irregularity strength Total vertex irregularity strength Graph weighting Graph labelling |
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