On graphs with linear convergence

BONOMO, FLAVIA; FRÍAS ARMENTA, MARTÍN; TARAVILSE, LEOPOLDO

La Plata

Workshop; VII Latin-American Workshop on Cliques in Graphs; 2016

UNLP

Iterated clique graphs, whether they diverge or converge, tend to have an explosive behaviour in the first few steps. That is why in [Larrión, Neumann-Lara, 2002] the authors showed for the first time a class of graphs with linear divergence with respect to the number of vertices. In [Larrión, Pizaña, Villarroel-Flores, 2013], evidence is shown that the topology ofa graph is related with the k-behaviour. In this paper we will show two familiesof graphs, each of them closed and with linear convergence with respect to thenumber of vertices. In fact, the number of vertices is lowered by m with m at least 4 for the first family and m at least 3 for the second family, leaving the question of whether it exists or not a family of graphs that converge to a non-trivial graph decreasing the number of vertices by 1 or 2 in each step. The first family behaves like cylinders, and the second class like Möbius strips.