Based on the research results, the chromatic number of vertex coloring on dual graph of a wheel graph is: Keywords: Vertex Coloring, Chromatic Number, Dual Graph and Wheel Graph. The vertex coloring is obtained by determining the chromatic number of the dual graph of the wheel graph, determining the pattern of the chromatic number and giving the color. The result showed that the wheel graph is a self-dual graph because it is isomorphic with its dual graph, namely. This research starts from describing some wheel graph from to, then construct a dual graph from a wheel graph from to, then gives color to the vertices of the dual graph by determining the chromatic number. Berdasarkan hasil penelitian, diperoleh bilangan kromatik pewarnaan titik pada graf dual dari graf roda yakni Kata Kunci: Pewarnaan Titik, Bilangan Kromatik, Graf Dual dan Graf Roda.This research aims to construct a dual graph from a wheel graph (Wn*) and determine the dual graph chromatic number of the wheel graph (Wn*).
Pewarnaan titik diperoleh dengan menentukan bilangan kromatik graf dual dari graf roda, menentukan pola dari bilangan kromatik, dan memberikan warna. Diperoleh hasil bahwa Graf roda merupakan graf self-dual karena isomorfik dengan graf dualnya yaitu. Penelitian ini dimulai dari menggambarkan beberapa graf roda dari ke, kemudian membangun graf dual dari graf roda dengan memanfaatkan graf-graf dari ke, kemudian memberikan warna pada titik-titik dari graf dualnya dengan menentukan bilangan kromatiknya. Penelitian ini bertujuan mengkonstruksi graf dual dari graf roda (Wn*) dan menentukan bilangan kromatik graf dual dari graf roda (Wn*). Besides, we also demonstrate that using bi-directional encoder representation from transformer (BERT) model further boosts the performance of the SLU task. Experiments show that our proposed approach is superior to multiple baselines on ATIS and SNIPS datasets. The two tasks promote each other and carry out end-to-end training at the same time. Intent nodes can provide utterance-level semantic information for slot filling, while slot nodes can also provide local keyword information for intent detection. To construct a graph structure for utterances, we create intent nodes, slot nodes, and directed edges. Therefore, we combine these two advantages and propose a new joint model with a wheel-graph attention network (Wheel-GAT), which is able to model interrelated connections directly for single intent detection and slot filling. In addition, graph neural network has made good achievements in the field of vision. In order to model these two tasks at the same time, many joint models based on deep neural networks have been proposed recently and archived excellent results. Intent detection and slot filling are recognized as two very important tasks in a spoken language understanding (SLU) system.
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