Certain types of ladder prime graphicable algebras

This investigation comprises the continuation of creative research in Discrete Mathematics presented in previous papers on algebras in general, regarding the utilization of graphs to contemplate the specific instance of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are especially fascinating since they are intrinsically connected with other Mathematical fields, for example, grouptheory, stochastics processes and dynamical systems. Depiction on primeness of particular type of graphicable and subgraphicable algebras is described in view of the newline of research initiated previously by some of the authors.