TY - JOUR ID - 53432 TI - The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Anaya, José G. AU - Cano, Alfredo AU - Castañeda-Alvarado, Enrique AU - Castillo-Rubí, Marco A. AD - Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México. Y1 - 2018 PY - 2018 VL - 4 IS - 1 SP - 13 EP - 27 KW - Hyperspaces KW - symmetric product KW - finite graph KW - homotopy DO - 10.22034/kjm.2017.53432 N2 - 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. UR - https://www.kjm-math.org/article_53432.html L1 - https://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf ER -