Jaco-type graphs and black energy dissipation

Authors
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Feb 21, 2017
Volume
8
Issue
2
Pages
141–152
Identifiers
DOI: 10.1515/apam-2016-0056
Source
De Gruyter
Keywords
In this paper, we introduce the notion of an energy graph G of order n ∈ ℕ ${n\in\mathbb{N}}$ . Energy graphs are simple, connected and finite directed graphs. The vertices, labelled u 1 , u 2 , … , u n ${u_{1},u_{2},\dots,u_{n}}$ , are such that ( u i , u j ) ∉ A ⁢ ( G ) ${(u_{i},u_{j})\notin A(G)}$ for all arcs ( u i , u j ) ${(u_{i},u_{j})}$ with i > j ${i>j}$ . 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.