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 {an} in general such that an∈N and an+1≥an, n=1,2,3,…,  a new population of directed graphs is defined such that for a given sequence {an} the infinite directed root-graph has d+(vn)=an. The infinite directed root-graph is denoted J∞({an}). The family of finite Jaco-Type graphs is the set of directed graphs Jn({an}), n∈N by lobbing off all vertices and arcs in J∞({an}) for vertices vi, i>n. We present introductory results for two families of these new directed graphs.

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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).

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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 Article

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