The Behavior of Weighted Graph’s Orbit and Its Energy

Abstract

Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the weighted graph's orbit allows us to have a better understanding to the behaviour of the systems (graphs) during determined time and environment. Moreover, the energy of the graph's orbit is given.