Fundamental groups of iterated line graphs
DOI:
https://doi.org/10.14419/gjma.v2i1.1489Abstract
in this article, the Euler characteristic of the iterated line graph and its complement is studied.
References
M. Aigner, "Graphs whose complement and line graph are isomorphic", J. of Combinatorial Theory 7 (1969) 273-275.
J. Bondy, U. Murty, Graph theory with applications, New York: Macmillan; 1976.
R. Ducke, "How is a graph's Betti number related to its genus?", The American Mathematical Monthly, Vol. 78, No. 4. (1971) 386-388.
A. Hatcher, Algebraic topology, Cambridge University Press; 2001.
R. Han, L. Gang, "Survey of maximum genus of graphs", J. of East China Normal University, No. 5 (2010), 1 – 19.
M. Kotrbeık, M. Skoviera, Matchings, "cycle bases, and the maximum genus of a graph", the electronic j. of combinatorics 19(3) (2012), #P3.
F. Larrión, M. Pizaña, R. Villarroel-Flores, "The fundamental group of the clique graph", European J. Combin. 30 (2009) 288-294.
M. Imbert, "Fundamental groups of fat graphs", Note di Matematica Vol. 19, No. 2(1999) 257-268.
W. Massy, Algebraic topology: An introduction. Harcourt, Brace & World, New York; 1967.
S. Nada, E. H. Hamouda, "Fundamental group of dual graphs and applications to quantum space-time", Chaos, Solitons and Fractals 42 (2009) 500-503.
B. Schwartz, "On Interchange Graphs", pacific J. of Mathematics, Vol. 27,No. 2.; (1968) 393-396.
J. Stallings, "Topology of Finite Graphs", Invent. Math. 71, 551-565 (1983).
A. van Roij, H. Wilf, "The Interchange Graph of a finite graph", Acta. Math. 16, (1983) 263-269.
D. Zhou, R. Hao, W. He, "Lower bounds for the maximum genus of 4-regular graphs", Turk J Math 36 (2012), 530 – 537.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).