On Rainbow Vertex Antimagic Coloring and Its Application on STGNN Time Series Forecasting on Subsidized Diesel Consumption.

Let G = (V,E) be a simple, connected and un-directed graph. We introduce a new notion of rainbow vertex antimagic coloring. This is a natural expansion of rainbow vertex coloring combined with antimagic labeling. For f: E(G) → {1, 2, . . ., |E(G)|}, the weight of a vertex v ∈ V (G) against f is wf (v) = Σe∈E(v)f(e), where E(v) is the set of vertices incident to v. The function f is called vertex antimagic edge labeling if every vertex has distinct weight. A path is considered to be a rainbow path if for each vertex u and v, all internal vertices on the u - v path have different weights. The rainbow vertex antimagic connection number of G, denoted by rvac(G), is the smallest number of colors taken over all rainbow colorings induced by rainbow vertex antimagic labelings of G. In this paper we aim to discover some new lemmas or theorems regarding to rvac(G). Furthermore, to see the robust application of rainbow vertex antimagic coloring, at the end of this paper we will illustrate the implementation of RVAC on spatial temporal graph neural networks (STGNN) multistep time series forecasting on subsidized diesel consumption of some petrol stations. [ABSTRACT FROM AUTHOR]