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Jaco-type graphs and black energy dissipation

  • Johan Kok , Naduvath K. Sudev EMAIL logo , Kaithavalappil P. Chithra und Augustine Mary
Veröffentlicht/Copyright: 21. Februar 2017
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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.

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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

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