Zamfirescu, Carol T. (2)-pancyclic graphs. (English) Zbl 1262.05090 Discrete Appl. Math. 161, No. 7-8, 1128-1136 (2013). Summary: We introduce the class of (2)-pancyclic graphs, which are simple undirected finite connected graphs of order \(n\) having exactly two cycles of length \(p\) for each \(p\) satisfying \(3\leq p\leq n\), analyze their properties, and give several examples of such graphs, among which are the smallest. Cited in 1 ReviewCited in 1 Document MSC: 05C38 Paths and cycles 05C40 Connectivity Keywords:pancyclic graphs PDF BibTeX XML Cite \textit{C. T. Zamfirescu}, Discrete Appl. Math. 161, No. 7--8, 1128--1136 (2013; Zbl 1262.05090) Full Text: DOI OpenURL References: [1] Bondy, J. A.; Murty, U. S.R., Graph theory with applications, (1976), North-Holland · Zbl 1226.05083 [2] Boros, E.; Caro, Y.; Füredi, Z.; Yuster, R., Covering non-uniform hypergraphs, J. Combin. Theory Ser. B, 82, 270-284, (2001) · Zbl 1026.05087 [3] Chen, G.; Lehel, J.; Jacobson, M. S.; Shreve, W. E., Note on graphs without repeated cycle lengths, J. Graph Theory, 29, 1, 11-15, (1998) · Zbl 0919.05030 [4] G. Exoo, http://ginger.indstate.edu/ge/Graphs/PANCYCLIC/index.html (date when the reference was last accessed: 17.06.2011). [5] Lai, C., On the size of graphs with all cycles having distinct lengths, Discrete Math., 122, 363-364, (1993) · Zbl 0790.05046 [6] Lai, C., Graphs without repeated cycle lengths, Australas. J. Combin., 27, 101-105, (2003) · Zbl 1022.05038 [7] Markström, K., A note on uniquely pancyclic graphs, Australas. J. Combin., 44, 105-110, (2009) · Zbl 1177.05060 [8] Shi, Y., Some theorems of uniquely pancyclic graphs, Discrete Math., 59, 167-180, (1986) · Zbl 0589.05046 [9] Shi, Y., On maximum cycle-distributed graphs, Discrete Math., 71, 57-71, (1988) · Zbl 0654.05048 [10] Shi, Y.; Sun, J., Two results on uniquely \(r\)-pancyclic graphs, Chinese Quart. J. Math., 7, 2, 56-60, (1992), (in Chinese) · Zbl 0983.05500 [11] Shi, Y.; Sun, J., On uniquely \(r\)-bipancyclic graphs, J. Shanghai Teachers Univ., 26, 4, 1-10, (1997) [12] Shi, Y.; Yap, H. P.; Teo, S. K., On uniquely \(r\)-pancyclic graphs, Ann. New York Acad. Sci., 576, 487-499, (1989) · Zbl 0792.05088 [13] Sun, J., Some results on uniquely \(r\)-pancyclic graphs, J. Nanjing Univ. Nat. Sci. Ed., 27, special issue, 165-166, (1991), (in Chinese) · Zbl 0762.05062 [14] Sun, H.; Shi, Y.; Sun, J., A theorem of uniquely bipancyclic graphs, J. Shanghai Teachers Univ., 29, 4, 24-34, (2000) [15] Yap, H. P.; Teo, S. K., On uniquely \(r\)-pancyclic graphs, Lecture Notes in Math., 1073, 334-335, (1984) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.