Affiliation:
1. Freie Universität Berlin, Institut für Informatik, Berlin, Germany
2. Université Libre de Bruxelles, Computer Science Dept., Algorithms Research Group, Brussels, Belgium
Abstract
Albertson [3] has defined the P irregularity of a simple undirected graph G =
(V,E) as irr(G) =?uv?E |dG(u)- dG(v)|, where dG(u) denotes the degree of
a vertex u ? V. Recently, this graph invariant gained interest in the
chemical graph theory, where it occured in some bounds on the first and the
second Zagreb index, and was named the third Zagreb index [12]. For general
graphs with n vertices, Albertson has obtained an asymptotically tight upper
bound on the irregularity of 4n3/27: Here, by exploiting a different approach
than in [3], we show that for general graphs with n vertices the upper bound
?n/3? ?2n/3? (?2n/3? -1) is sharp. We also present lower bounds on
the maximal irregularity of graphs with fixed minimal and/or maximal vertex
degrees, and consider an approximate computation of the irregularity of a
graph.
Publisher
National Library of Serbia
Cited by
37 articles.
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