Abstract
Denote by λ 1( G) the largest eigenvalue of a real (0, 1)-adjacency matrix of a graph G, and by d̄( G) the mean degree of G. Collatz and Sinogowitz proposed λ 1( G)– d̄( G) as a measure of irregularity of G. A second such measure is the variance of the vertex degrees of G. The most irregular graphs according to these measures are determined for certain classes of graphs, and the two measures are shown to be incompatible for some pairs of graphs.
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