Chartrand, Gary; Oellermann, Ortrud R.; Saba, Farrokh; Zou, Hung Bin The uniformity number of a graph. (English) Zbl 0657.05043 Indian J. Math. 28, 1-7 (1986). The uniformity number of a graph G is the least positive integer n for which there exists a supergraph H of G satisfying: (i) the sets of degrees of the vertices of G and H are the same, (ii) for every nonnegative integer r, H contains either n or no vertices of degree r. The uniformity number of many complete bipartite and caterpillar graphs are determined. MSC: 05C35 Extremal problems in graph theory Keywords:complete bipartite graphs; uniformity number; supergraph; caterpillar graphs PDFBibTeX XMLCite \textit{G. Chartrand} et al., Indian J. Math. 28, 1--7 (1986; Zbl 0657.05043)