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) = Σ...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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International Association of Engineers
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113568/1/113568.pdf |
| _version_ | 1817927955004784640 |
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| author | Dafik Mursyidah, Indah Lutfiyatul Agustin, Ika Hesti Baihaki, Rifki Ilham Febrinanto, Falih Gozi Said Husain, Sharifah Kartini Sunder, R. |
| author_facet | Dafik Mursyidah, Indah Lutfiyatul Agustin, Ika Hesti Baihaki, Rifki Ilham Febrinanto, Falih Gozi Said Husain, Sharifah Kartini Sunder, R. |
| author_sort | Dafik |
| collection | UPM |
| description | 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. © (2024), (International Association of Engineers). All Rights Reserved. |
| first_indexed | 2024-12-09T02:26:39Z |
| format | Article |
| id | upm.eprints-113568 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-12-09T02:26:39Z |
| publishDate | 2024 |
| publisher | International Association of Engineers |
| record_format | dspace |
| spelling | upm.eprints-1135682024-11-26T04:32:23Z http://psasir.upm.edu.my/id/eprint/113568/ On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption Dafik Mursyidah, Indah Lutfiyatul Agustin, Ika Hesti Baihaki, Rifki Ilham Febrinanto, Falih Gozi Said Husain, Sharifah Kartini Sunder, R. 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. © (2024), (International Association of Engineers). All Rights Reserved. International Association of Engineers 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/113568/1/113568.pdf Dafik and Mursyidah, Indah Lutfiyatul and Agustin, Ika Hesti and Baihaki, Rifki Ilham and Febrinanto, Falih Gozi and Said Husain, Sharifah Kartini and Sunder, R. (2024) On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption. IAENG International Journal of Applied Mathematics, 54 (5). pp. 984-996. ISSN 1992-9978; eISSN: 1992-9986 https://www.iaeng.org/IJAM/issues_v54/issue_5/IJAM_54_5_22.pdf |
| spellingShingle | Dafik Mursyidah, Indah Lutfiyatul Agustin, Ika Hesti Baihaki, Rifki Ilham Febrinanto, Falih Gozi Said Husain, Sharifah Kartini Sunder, R. On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title | On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title_full | On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title_fullStr | On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title_full_unstemmed | On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title_short | On rainbow vertex antimagic coloring and its application on STGNN time series forecasting on subsidized diesel consumption |
| title_sort | on rainbow vertex antimagic coloring and its application on stgnn time series forecasting on subsidized diesel consumption |
| url | http://psasir.upm.edu.my/id/eprint/113568/1/113568.pdf |
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