Jaco-Type Graphs and Black Energy Dissipation

TL;DR

This paper introduces energy graphs, a new concept modeling energy transfer and dissipation in directed graphs, with a focus on Jaco-type graphs, and defines black energy dissipation and black arc number.

Contribution

It presents the novel concepts of energy graphs, black energy dissipation, and black arc number, specifically applied to Jaco-type graphs, expanding graph theory with energy transfer models.

Findings

Defined energy graphs with energy transfer rules.

Introduced black energy dissipation as a new graph property.

Applied concepts specifically to Jaco-type graphs.

Abstract

In this paper, we introduce the notion of an energy graph as a simple, directed and vertex labeled graph $G$ such that the arcs $(v_i, v_j) \notin A(G)$ if $i > j$ for all distinct pairs $v_i,v_j$ and at least one vertex $v_k$ exists such that $d^-(v_k)=0$. 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 result in energy dissipation. This dissipated energy is called black energy. 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.