P3-Carathéodory in Circulating Graphs

The maximization of influence in networks is a problem of great interest in several networks
In other areas, several models have been proposed to analyze this diffusion. Convexity in graphs is a
of these models, relying on several parameters to analyze the dynamics of this behavior,
such as envelope number, Radon, interval among others. Carathéodory's number is a
of these interesting parameters, already shown to be NP-Complete, of the study of the behavior of
diffusion of influence. In this article we will deal with the Carathéodory number for graphs circulating in
convexity P3. For circulating graphs Cn({1, r}) with r = 2, we find that the number de
Carathéodory is c(C_n(1,2)) = 2, so we find the number of Carathéodory
for the graph subclass Cycle Power, i.e. c(C^k_n) = 2. For C_n(1,r) with r>2 and n≥4r−2 we show that c(Cn(1, r))≥⌊(2r+1)/3⌋