A Study on Jaco-Type Graphs

Authors

  • Johan Kok Tshwane Metropolitan Police Department, City of Tshwane
  • N. K. Sudev Department of Mathematics, Vidya Academy of Science & Technology, Thalakkottukara, Thrissur 680501
  • K. P. Chithra Naduvath Mana, Nandikkara, Thrissur 680301

DOI:

https://doi.org/10.26713/jims.v8i2.407

Keywords:

Jaco graph, Linear Jaco graph, Jaco-type graph

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.

Downloads

Download data is not yet available.

References

J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan Press, London (1976).

A. Brandstädt, V.B. Le and J.P. Spinrad, Graph classes: A Survey, SIAM, Philadelphia (1999).

G. Chartrand and L. Lesniak, Graphs and Digraphs, CRC Press (2000).

F. Harary, Graph Theory, Addison-Wesley Publishing Company, London (1969).

J. Kok, P. Fisher, B. Wilkens, M. Mabula and V. Mukungunugwa, Characteristics of finite Jaco graphs, (J_n(1)), (n inmathbb{N}), arXiv: 1404.0484v1 [math.CO].

J. Kok, P. Fisher, B. Wilkens, M. Mabula and V. Mukungunugwa, Characteristics of Jaco graphs, (J_infty(a)), (ainmathbb{N}), arXiv: 1404.1714v1 [math.CO], 7 April 2014.

J. Kok, C. Susanth and S.J. Kalayathankal, A study on linear Jaco graphs, J. Informatics & Math. Sci. 7 (2) (2015), 69–80.

J. Kok, Linear Jaco graphs: A critical review, J. Informatics & Math. Sci. 8 (2) (2016), 67–103.

D.B. West, Introduction to Graph Theory, Pearson Education Inc. (2001).

Downloads

Published

2016-05-24
CITATION

How to Cite

Kok, J., Sudev, N. K., & Chithra, K. P. (2016). A Study on Jaco-Type Graphs. Journal of Informatics and Mathematical Sciences, 8(2), 105–112. https://doi.org/10.26713/jims.v8i2.407

Issue

Vol. 8 No. 2 (2016)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.