@article { author = {Anaya, José G. and Cano, Alfredo and Castañeda-Alvarado, Enrique and Castillo-Rubí, Marco A.}, title = {The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint}, journal = {Khayyam Journal of Mathematics}, volume = {4}, number = {1}, pages = {13-27}, year = {2018}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {10.22034/kjm.2017.53432}, abstract = {This paper describes the classification of the $n$-fold symmetric product of a finite graph by means of its homotopy type, having as universal models the $n$-fold symmetric product of the wedge of $n$-circles; and introduces a CW-complex called $binomial\ torus$, which is homeomorphic to a space that is a strong deformation retract of the second symmetric products of the wedge of $n$-circles. Applying the above we calculate the fundamental group, Euler characteristic, homology and cohomology groups of the second symmetric product of finite graphs.}, keywords = {Hyperspaces,symmetric product,finite graph,homotopy}, url = {https://www.kjm-math.org/article_53432.html}, eprint = {https://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf} }