A Study on Jaco-Type Graphs

Johan Kok, N. K. Sudev, K. P. Chithra

Abstract


For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(n=1,2,3,\ldots\),  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 \(J_\infty(\{a_n\})\). 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 \(J_\infty(\{a_n\})\) for vertices \(v_i\), \(i > n\). We present introductory results for two families of these new directed graphs.

Keywords


Jaco graph; Linear Jaco graph; Jaco-type graph

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v8i2.407

eISSN 0975-5748; pISSN 0974-875X