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Extremely irregular graphs. (English) Zbl 1299.05060

Summary: The irregularity of a graph \(G\) is defined as \(\operatorname{irr}(G)=\sum| d(x)-d(y)| \) where \(d(x)\) is the degree of vertex \(x\) and the summation embraces all pairs of adjacent vertices of \(G\). We characterize the graphs minimum and maximum values of \(\operatorname{irr}\).

MSC:

05C07 Vertex degrees
05C05 Trees
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Online Encyclopedia of Integer Sequences:

a(n) = floor(n/3)*(n - floor(n/3))*(n - floor(n/3) - 1).