2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163848In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $α_1$, a new vertex $x_t$ and $m$ edges incident with $x_t$ are added; or, with probability $α-α_1$, $m$ edges are added; or finally, with probability $1-\a$, $m$ random edges are deleted. Note that in any case edges are added in the manner of preferential attachment. we prove that there exists a critical point $α_c$ satisfying: 1) if $α_1<α_c$, then the model has power law degree sequence; 2) if $α_1>α_c$, then the model has exponential degree sequence; and 3) if $α_1=α_c$, then the model has a degree sequence lying between the above two cases.18 pagesProbabilityHistory and Overview05C07, 05C80text