A Study on The Quadratic Jaco Graph

Authors

  • R. Jayasree Department of Mathematics, Nirmala College for Women, Coimbatore
  • A. Kulandai Therese Department of Mathematics, Nirmala College for Women, Coimbatore
  • U. Mary Department of Mathematics, Nirmala College for Women, Coimbatore
  • Johan Kok Tshwane Metropolitan Police Department, City of Tshwane

DOI:

https://doi.org/10.26713/cma.v9i4.460

Keywords:

Colouring sum of graphs, Chromatic variance, Chromatic mean, Directed graph, Hope graph, Jaco graph, Jaconian vertex, Jaconian set

Abstract

In this paper we introduce the quadratic Jaco graph. The characteristics, properties and some graph invariants of quadratic Jaco graphs are also discussed. The observation that quadratic Jaco graphs are well-structured in respect of complete graphs and bridges led to the notion of braided complete graphs.

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Author Biography

R. Jayasree, Department of Mathematics, Nirmala College for Women, Coimbatore

Director: Licensing Services, City of Tshwane

References

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

G. Chartrand and P. Zang, Chromatic Graph Theory, CRC Press (2009).

T.R. Jensen and B. Toft, Graph Coloring Problems, John Wiley & Sons (1995).

J. Kok, P. Fisher, B. Wilkens, M. Mabula and V. Mukungunungwa, Characteristics of finite Jaco graphs, $J_n(1)$, $n in N$, arXiv: 1404.0484v1 [math.CO], 2 April 2014.

J. Kok, P. Fisher, B. Wilkens, M. Mabula and V. Mukungunungwa, Characteristics of Jaco graphs, $J_1(a)$, $n in N$, arXiv: 1404.0484v1 [math.CO], 7 April 2014.

J. Kok, C. Susanth and S.J. Kalayathankal, A study on linear Jaco graphs, Journal of Informatics and Mathematical Sciences 7(2) (2015), 69 – 80, DOI: 10.26713/jims.v7i2.291.

J. Kok, Linear Jaco graphs: A critical review, Journal of Informatics and Mathematical Sciences 8(2) (2016), 67 – 103, DOI: 10.26713/jims.v8i2.402.

J. Kok, N.K. Sudev and K.P. Chithra, General colouring sums of graphs, Cogent Mathematics 3 (2016), article ID 1140002, pages 11, DOI: 10.1080/23311835.2016.1140002.

N.K. Sudev, S. Satheesh, K.P. Chithra and J. Kok, On Certain Colouring Parameters of Graphs, communicated.

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Published

25-12-2018
CITATION

How to Cite

Jayasree, R., Therese, A. K., Mary, U., & Kok, J. (2018). A Study on The Quadratic Jaco Graph. Communications in Mathematics and Applications, 9(4), 567–580. https://doi.org/10.26713/cma.v9i4.460

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

License

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