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On the irregularity strength of trees
Author(s) -
Bohman Tom,
Kravitz David
Publication year - 2004
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10158
Subject(s) - combinatorics , mathematics , graph , lambda , upper and lower bounds , discrete mathematics , physics , mathematical analysis , optics
For any graph G , let n i be the number of vertices of degree i , and $\lambda (G)={max} _{i\le j}\{ {n_i+\cdots +n_j+i-1\over j}\}$ . This is a general lower bound on the irregularity strength of graph G . All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite sequence of trees with λ( T ) =  n 1 but strength converging to ${11-\sqrt 5\over 8} n_1$ . © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 241–254, 2004

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