Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter February 21, 2017

Jaco-type graphs and black energy dissipation

  • Johan Kok , Naduvath K. Sudev EMAIL logo , Kaithavalappil P. Chithra and Augustine Mary

Abstract

In this paper, we introduce the notion of an energy graph G of order n. Energy graphs are simple, connected and finite directed graphs. The vertices, labelled u1,u2,,un, are such that (ui,uj)A(G) for all arcs (ui,uj) with i>j. Initially, equal amount of potential energy is allocated to certain vertices. Then, at a point of time, these vertices transform the potential energy into kinetic energy and initiate transmission to head vertices. Upon reaching a head vertex, perfect elastic collisions with atomic particles take place and propagate energy further. Propagation rules apply which could result in energy dissipation. The total dissipated energy throughout the graph is called the black energy of the graph. The notion of the black arc number of a graph is also introduced in this paper. Mainly Jaco-type graphs are considered for the application of the new concepts.

Acknowledgements

The authors of this article gratefully acknowledge the critical and constructive comments of the anonymous referee, which significantly improved the content and presentation of this article.

References

[1] Bondy J. A. and Murty U. S. R., Graph Theory with Applications, Macmillan Press, London, 1976. 10.1007/978-1-349-03521-2Search in Google Scholar

[2] Chartrand G. and Lesniak L., Graphs and Digraphs, CRC Press, Boca Raton, 2000. Search in Google Scholar

[3] Cormen T. H., Leiserson C. E., Rivest R. L. and Stein C., Topological sort, Introduction to Algorithms. Second Edition, MIT Press, Cambridge (2001), 549–552. Search in Google Scholar

[4] Fishburn P. C., Interval Orders and Interval Graphs, John Willey & Sons, New York, 1985. 10.1016/0012-365X(85)90042-1Search in Google Scholar

[5] Harary F., Graph Theory, Narosa Publishing, New Delhi, 2001. Search in Google Scholar

[6] Kok J., Linear Jaco graphs: A critical review, J. Inf. Math. Sci. 8 (2016), no. 2, 67–103. Search in Google Scholar

[7] Kok J., Fisher P., Wilkens B., Mabula M. and Mukungunugwa V., Characteristics of finite Jaco graphs, Jn(1),n, preprint 2014, https://arxiv.org/abs/1404.0484v1. Search in Google Scholar

[8] Kok J., Fisher P., Wilkens B., Mabula M. and Mukungunugwa V., Characteristics of Jaco graphs, J(a),a, preprint 2014, https://arxiv.org/abs/1404.1714v1. Search in Google Scholar

[9] Kok J. and Sudev N. K., A study on primitive holes of certain graphs, Int. J. Sci. Eng. Res. 6 (2015), no. 3, 631–635. Search in Google Scholar

[10] Kok J., Sudev N. K. and Chithra K. P., A study on Jaco-type graphs, J. Inf. Math. Sci. 8 (2016), no. 2, 105–112. Search in Google Scholar

[11] Kok J., Susanth C. and Kalayathankal S. J., A study on linear Jaco graphs, J. Inf. Math. Sci. 7 (2015), no. 2, 69–80. Search in Google Scholar

[12] Luce R. D., Semiorders and a theory of utility discrimination, Econometrica 24 (1956), 178–191. 10.2307/1905751Search in Google Scholar

[13] West D. B., Introduction to Graph Theory, Pearson Education, Delhi, 2001. Search in Google Scholar

Received: 2016-6-21
Revised: 2017-1-15
Accepted: 2017-1-20
Published Online: 2017-2-21
Published in Print: 2017-4-1

© 2017 by De Gruyter

Downloaded on 31.5.2024 from https://www.degruyter.com/document/doi/10.1515/apam-2016-0056/html
Scroll to top button