A Study on Jaco-Type Graphs - Kok, Johan; Sudev, N. K.; Chithra, K. P. (Journal of Informatics and Mathematical Sciences, 2016)
For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(n=1,2,3,…\), a new population of directed graphs is defined such that for a given sequence \(\{a_n\}\) the infinite directed root-graph has \(d^+(v_n)=a_n\). The infinite directed root-graph is denoted \(J_∞(\{a_n\})\). The family of finite Jaco-Type graphs is the set of directed graphs \(J_n(\{a_n\})\), \(n\in \mathbb{N}\) by lobbing off all vertices and arcs in \(J_∞(\{a_n\})\) for vertices \(v_i\), \(i > n\). We present introductory results for two families of these new directed graphs.