Khodkar, Abdollah; Sawin, Oliver; Mueller, Lisa; Choi, Won Hyuk \((r)\)-pancyclic, \((r)\)-bipancyclic and oddly \((r)\)-bipancyclic graphs. (English) Zbl 1377.05092 J. Comb. Math. Comb. Comput. 102, 267-275 (2017). Summary: A graph with \(v\) vertices is \((r)\)-pancyclic if it contains precisely \(r\) cycles of every length from 3 to \(v\). A bipartite graph with even number of vertices \(v\) is said to be \((r)\)-bipancyclic if it contains precisely \(r\) cycles of each even length from 4 to \(v\). A bipartite graph with odd number of vertices \(v\) and minimum degree at least 2 is said to be oddly \((r)\)-bipancyclic if it contains precisely \(r\) cycles of each even length from 4 to \(v-1\). In this paper, using a computer search, we classify all \((r)\)-pancyclic and \((r)\)-bipancyclic graphs, \(r\geq 2\), with \(v\) vertices and at most \(v+5\) edges. We also classify all oddly \((r)\)-bipancyclic graphs, \(r\geq 1\), with \(v\) vertices and at most \(v+4\) edges. MSC: 05C38 Paths and cycles PDFBibTeX XMLCite \textit{A. Khodkar} et al., J. Comb. Math. Comb. Comput. 102, 267--275 (2017; Zbl 1377.05092) Full Text: arXiv